Publications

Detailed research profiles of me and my work, including citation and impact factor statistics, are available at

Reviews of my publications are available on

See also

The full text of each of my articles listed here is available in pdf and other formats—just follow the links provided to the math arxiv for preprints or to the journal itself for the published version, if this is available.

(Due to technical difficulties with a plugin connecting to the database, only 65 publications will appear; I am working on it.)

  • Every countable model of arithmetic or set theory has a pointwise definable end extension
    • [DOI] J. D. Hamkins, “Every countable model of arithmetic or set theory has a pointwise definable end extension,” mathematics arXiv, 2022.
      [Bibtex]
      @ARTICLE{Hamkins:Every-countable-model-of-arithmetic-or-set-theory-has-a-pointwise-definable-end-extension,
      author = {Joel David Hamkins},
      title = {Every countable model of arithmetic or set theory has a pointwise definable end extension},
      journal = {mathematics arXiv},
      year = {2022},
      volume = {},
      number = {},
      pages = {},
      month = {},
      note = {},
      abstract = {},
      keywords = {},
      source = {},
      doi = {10.48550/ARXIV.2209.12578},
      eprint = {2209.12578},
      archivePrefix={arXiv},
      primaryClass={math.LO},
      url = {http://jdh.hamkins.org/pointwise-definable-end-extensions},
      }
    • V. Gitman and J. D. Hamkins, “Every model of arithmetic or set theory of size at most continuum has a Leibnizian extension,” , 2022.
      [Bibtex]
      @article{GitmanHamkins:Every-model-of-arithmetic-or-set-theory-size-at-most-continuum-has-Leibnizian-extension,
      author = {Victoria Gitman and Joel David Hamkins},
      title = {Every model of arithmetic or set theory of size at most continuum has a Leibnizian extension},
      note = {in preparation},
      year = {2022},
      }
    • [DOI] J. D. Hamkins, “Fregean abstraction in Zermelo-Fraenkel set theory: a deflationary account,” Mathematics arXiv, 2022.
      [Bibtex]
      @article{Hamkins:Fregean-abstraction-deflationary-account,
      author = {Hamkins, Joel David},
      title = {Fregean abstraction in Zermelo-Fraenkel set theory: a deflationary account},
      doi = {10.48550/ARXIV.2209.07845},
      eprint = {2209.07845},
      archivePrefix={arXiv},
      primaryClass={math.LO},
      journal = {Mathematics arXiv},
      year = {2022},
      url = {http://jdh.hamkins.org/fregean-abstraction-deflationary-account},
      }
    • J. D. Hamkins, Infinite Games, Frivoloties of the Gods, , 2022, book in preparation.
      [Bibtex]
      @BOOK{Hamkins:Infinite-Games,
      author = {Joel David Hamkins},
      editor = {},
      title = {Infinite Games, Frivoloties of the Gods},
      publisher = {},
      year = {2022},
      volume = {},
      number = {},
      series = {},
      address = {},
      edition = {},
      month = {},
      note = {book in preparation},
      abstract = {},
      isbn = {},
      price = {},
      keywords = {noCV},
      source = {},
      }
    • K. Knudson, E. Lamb, and J. D. Hamkins, My Favorite Theorem, podcast interview, transcript available , episode 70, September, 2021.
      [Bibtex]
      @MISC{KnudsonLambHamkins2021:My-favorite-theorem-podcast-interview,
      author = {Kevin Knudson and Evelyn Lamb and Joel David Hamkins},
      title = {My Favorite Theorem},
      howpublished = {podcast interview, transcript available},
      year = {2021},
      month = {September},
      note = {episode 70},
      url = {https://podbay.fm/p/my-favorite-theorem/e/1632318596},
      }
    • J. D. Hamkins and B. Yao, “Reflection in second-order set theory with abundant urelements bi-interprets a supercompact cardinal,” Mathematics arXiv, 2022.
      [Bibtex]
      @ARTICLE{HamkinsYao:Reflection-in-second-order-set-theory-with-abundant-urelements,
      author={Joel David Hamkins and Bokai Yao},
      year={2022},
      eprint={2204.09766},
      archivePrefix={arXiv},
      primaryClass={math.LO},
      title = {Reflection in second-order set theory with abundant urelements bi-interprets a supercompact cardinal},
      journal = {Mathematics arXiv},
      volume = {},
      number = {},
      pages = {},
      month = {},
      note = {manuscript under review},
      abstract = {},
      keywords = {under-review},
      source = {},
      doi = {},
      url = {http://jdh.hamkins.org/second-order-reflection-with-abundant-urelements},
      }
    • J. D. Hamkins, “Infinite Wordle and the mastermind numbers,” Mathematics arXiv, 2022.
      [Bibtex]
      @ARTICLE{Hamkins:Infinite-Wordle-and-the-mastermind-numbers,
      author = {Joel David Hamkins},
      title = {Infinite Wordle and the mastermind numbers},
      journal = {Mathematics arXiv},
      year = {2022},
      volume = {},
      number = {},
      pages = {},
      month = {},
      note = {Under review},
      abstract = {},
      keywords = {under-review},
      source = {},
      doi = {},
      eprint = {2203.06804},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://jdh.hamkins.org/infinite-wordle-mastermind},
      }
    • J. D. Hamkins and D. Leonessi, “Infinite Hex is a draw,” Mathematics arXiv, 2022.
      [Bibtex]
      @ARTICLE{HamkinsLeonessi:Infinite-Hex-is-a-draw,
      author = {Joel David Hamkins and Davide Leonessi},
      title = {Infinite Hex is a draw},
      journal = {Mathematics arXiv},
      year = {2022},
      volume = {},
      number = {},
      pages = {},
      month = {},
      note = {Under review},
      abstract = {},
      keywords = {under-review},
      source = {},
      doi = {},
      eprint = {2201.06475},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://jdh.hamkins.org/infinite-hex-is-a-draw},
      }
    • [DOI] J. D. Hamkins, Nonlinearity and illfoundedness in the hierarchy of large cardinal consistency strength arXiv, 2022.
      [Bibtex]
      @misc{Hamkins:Nonlinearity-in-the-hierarchy-of-large-cardinal-consistency-strength,
      author = {Joel David Hamkins},
      title = {Nonlinearity and illfoundedness in the hierarchy of large cardinal consistency strength},
      publisher = {arXiv},
      year = {2022},
      journal = {},
      volume = {},
      number = {},
      pages = {},
      doi = {10.48550/ARXIV.2208.07445},
      eprint = {2008.07445},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://jdh.hamkins.org/nonlinearity-in-the-hierarchy-of-consistency-strength},
      }
    • J. D. Hamkins and B. Yao, The surprising strength of reflection in second-order set theory with abundant atoms , in preparation.
      [Bibtex]
      @misc{HamkinsYao:Surprising-strength-of-reflection-with-abundant-atoms,
      author = {Joel David Hamkins and Bokai Yao},
      title = {The surprising strength of reflection in second-order set theory with abundant atoms},
      journal = {},
      year = {},
      volume = {},
      number = {},
      pages = {},
      month = {},
      note = {in preparation},
      abstract = {},
      keywords = {noCV},
      source = {},
      doi = {},
      }
    • T. Button and J. D. Hamkins, Credence of belief as a forcing relation , in preparation.
      [Bibtex]
      @misc{ButtonHamkins:Credence-as-a-forcing-relation,
      author = {Timothy Button and Joel David Hamkins},
      title = {Credence of belief as a forcing relation},
      note = {in preparation},
      keywords = {noCV},
      }
    • J. D. Hamkins and D. Leonessi, “Transfinite game values in infinite draughts,” Mathematics arXiv, 2021.
      [Bibtex]
      @ARTICLE{HamkinsLeonessi:Transfinite-game-values-in-infinite-draughts,
      author = {Joel David Hamkins and Davide Leonessi},
      title = {Transfinite game values in infinite draughts},
      journal = {Mathematics arXiv},
      year = {2021},
      volume = {},
      number = {},
      pages = {},
      month = {},
      note = {Under review},
      abstract = {},
      keywords = {under-review},
      source = {},
      doi = {},
      eprint = {2111.02053},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://jdh.hamkins.org/transfinite-game-values-in-infinite-draughts},
      }
    • A. Berarducci, A. Fornasiero, and J. D. Hamkins, “Is the twin prime conjecture independent of Peano Arithmetic?,” Mathematics arXiv, 2021.
      [Bibtex]
      @ARTICLE{BerarducciFornasieroHamkins:Is-the-twin-prime-conjecture-independent-of-PA,
      author = {Alessandro Berarducci and Antongiulio Fornasiero and Joel David Hamkins},
      title = {Is the twin prime conjecture independent of Peano Arithmetic?},
      journal = {Mathematics arXiv},
      year = {2021},
      volume = {},
      number = {},
      pages = {},
      month = {},
      note = {Under review},
      abstract = {},
      keywords = {under-review},
      source = {},
      doi = {},
      eprint = {2110.08640},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://jdh.hamkins.org/is-the-twin-prime-conjecture-independent-of-peano-arithmetic/},
      }
    • J. D. Hamkins, My view of Univ , The Martlet, Issue 11, Spring 2020, University College, Oxford, 2020.
      [Bibtex]
      @MISC{Hamkins2020:My-view-of-univ,
      author = {Joel David Hamkins},
      title = {My view of Univ},
      howpublished = {},
      year = {2020},
      month = {},
      note = {The Martlet, Issue 11, Spring 2020, University College, Oxford},
      abstract = {},
      keywords = {noCV},
      source = {},
      url = {https://t.co/3tqVwfD4uZ},
      }
    • J. D. Hamkins, R. Miller, and K. J. Williams, “Forcing as a computational process,” Mathematics ArXiv, 2020.
      [Bibtex]
      @ARTICLE{HamkinsMillerWilliams:Forcing-as-a-computational-process,
      author = {Joel David Hamkins and Russell Miller and Kameryn J. Williams},
      title = {Forcing as a computational process},
      journal = {Mathematics ArXiv},
      year = {2020},
      volume = {},
      number = {},
      pages = {},
      month = {},
      note = {Under review},
      abstract = {},
      keywords = {under-review},
      source = {},
      doi = {},
      url = {http://jdh.hamkins.org/forcing-as-a-computational-process},
      eprint = {2007.00418},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      }
    • J. D. Hamkins and R. Solberg, “Categorical large cardinals and the tension between categoricity and set-theoretic reflection,” Mathematics ArXiv, 2020.
      [Bibtex]
      @ARTICLE{HamkinsSolberg:Categorical-large-cardinals,
      author = {Joel David Hamkins and Robin Solberg},
      title = {Categorical large cardinals and the tension between categoricity and set-theoretic reflection},
      journal = {Mathematics ArXiv},
      year = {2020},
      volume = {},
      number = {},
      pages = {},
      month = {},
      note = {Under review},
      abstract = {},
      keywords = {under-review},
      url = {http://jdh.hamkins.org/categorical-large-cardinals/},
      source = {},
      doi = {},
      eprint = {2009.07164},
      archivePrefix ={arXiv},
      primaryClass = {math.LO}
      }
    • J. D. Hamkins and W. A. Wołoszyn, “Modal model theory,” Mathematics ArXiv, 2020.
      [Bibtex]
      @ARTICLE{HamkinsWoloszyn:Modal-model-theory,
      title={Modal model theory},
      author={Joel David Hamkins and Wojciech Aleksander Wołoszyn},
      journal = {Mathematics ArXiv},
      year={2020},
      eprint={2009.09394},
      archivePrefix={arXiv},
      primaryClass={math.LO},
      note = {Under review},
      abstract = {},
      keywords = {under-review},
      source = {},
      doi = {},
      }
    • R. Cutolo and J. D. Hamkins, “Choiceless large cardinals and set-theoretic potentialism,” Mathematical Logic Quarterly, p. 10 pages, 2022.
      [Bibtex]
      @ARTICLE{CutoloHamkins:Choiceless-large-cardinals-and-set-theoretic-potentialism,
      author = {Raffaella Cutolo and Joel David Hamkins},
      title = {Choiceless large cardinals and set-theoretic potentialism},
      journal = {Mathematical Logic Quarterly},
      year = {2022},
      volume = {},
      number = {},
      pages = {10 pages},
      month = {},
      note = {to appear},
      abstract = {},
      keywords = {},
      source = {},
      doi = {},
      url = {http://jdh.hamkins.org/choiceless-large-cardinals-and-set-theoretic-potentialism},
      eprint = {2007.01690},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      }
    • [DOI] A. R. Freire and J. D. Hamkins, “Bi-interpretation in weak set theories,” Journal of Symbolic Logic, vol. 86, iss. 2, 2021.
      [Bibtex]
      @ARTICLE{FreireHamkins2021:Bi-interpretation-in-weak-set-theories,
      author = {Alfredo Roque Freire and Joel David Hamkins},
      title = {Bi-interpretation in weak set theories},
      DOI={10.1017/jsl.2020.72},
      journal={Journal of Symbolic Logic},
      pages={609--634},
      year = {2021},
      volume = {86},
      number = {2},
      pages = {},
      month = {},
      note = {},
      abstract = {},
      keywords = {},
      source = {},
      url = {http://jdh.hamkins.org/bi-interpretation-in-weak-set-theories},
      eprint = {2001.05262},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      }
    • D. D. Blair, J. D. Hamkins, and K. O’Bryant, “Representing Ordinal Numbers with Arithmetically Interesting Sets of Real Numbers,” Integers, vol. 20A, 2020.
      [Bibtex]
      @ARTICLE{BlairHamkinsOBryant2020:Representing-ordinal-numbers-with-arithmetically-interesting-sets-of-real-numbers,
      author = {D. Dakota Blair and Joel David Hamkins and Kevin O'Bryant},
      title = {Representing Ordinal Numbers with Arithmetically Interesting Sets of Real Numbers},
      journal = {Integers},
      FJOURNAL = {Integers Electronic Journal of Combinatorial Number Theory},
      year = {2020},
      volume = {20A},
      number = {},
      pages = {},
      month = {},
      note = {Paper~A3, \url{http://math.colgate.edu/~integers/vol20a.html}},
      abstract = {},
      keywords = {},
      source = {},
      doi = {},
      url = {https://wp.me/p5M0LV-1Tg},
      eprint = {1905.13123},
      archivePrefix = {arXiv},
      primaryClass = {math.NT},
      }
    • J. D. Hamkins, Lectures on the Philosophy of Mathematics, MIT Press, 2021.
      [Bibtex]
      @BOOK{Hamkins2021:Lectures-on-the-philosophy-of-mathematics,
      author = {Joel David Hamkins},
      editor = {},
      title = {{Lectures on the Philosophy of Mathematics}},
      publisher = {MIT Press},
      year = {2021},
      volume = {},
      number = {},
      series = {},
      address = {},
      edition = {},
      month = {},
      note = {},
      abstract = {},
      isbn = {9780262542234},
      price = {},
      keywords = {book},
      source = {},
      url = {https://mitpress.mit.edu/books/lectures-philosophy-mathematics},
      }
    • [DOI] M. E. Habič, J. D. Hamkins, L. D. Klausner, J. Verner, and K. J. Williams, “Set-theoretic blockchains,” Archive for Mathematical Logic, 2019.
      [Bibtex]
      @ARTICLE{HabicHamkinsKlausnerVernerWilliams2018:Set-theoretic-blockchains,
      author = {Miha E. Habič and Joel David Hamkins and Lukas Daniel Klausner and Jonathan Verner and Kameryn J. Williams},
      title = {Set-theoretic blockchains},
      journal="Archive for Mathematical Logic",
      year="2019",
      month="Mar",
      day="26",
      abstract="Given a countable model of set theory, we study the structure of its generic multiverse, the collection of its forcing extensions and ground models, ordered by inclusion. Mostowski showed that any finite poset embeds into the generic multiverse while preserving the nonexistence of upper bounds. We obtain several improvements of his result, using what we call the blockchain construction to build generic objects with varying degrees of mutual genericity. The method accommodates certain infinite posets, and we can realize these embeddings via a wide variety of forcing notions, while providing control over lower bounds as well. We also give a generalization to class forcing in the context of second-order set theory, and exhibit some further structure in the generic multiverse, such as the existence of exact pairs.",
      issn="1432-0665",
      doi="10.1007/s00153-019-00672-z",
      note = {},
      abstract = {},
      eprint = {1808.01509},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      keywords = {},
      source = {},
      url = {http://wp.me/p5M0LV-1M8},
      }
    • [DOI] A. Enayat, J. D. Hamkins, and B. Wcisl o, “Topological models of arithmetic,” Fund. Math., vol. 256, iss. 2, p. 171–193, 2022.
      [Bibtex]
      @article {EnayatHamkinsWcislo2022:Topological-models-of-arithmetic,
      AUTHOR = {Enayat, Ali and Hamkins, Joel David and Wcis\l o, Bartosz},
      TITLE = {Topological models of arithmetic},
      JOURNAL = {Fund. Math.},
      FJOURNAL = {Fundamenta Mathematicae},
      VOLUME = {256},
      YEAR = {2022},
      NUMBER = {2},
      PAGES = {171--193},
      ISSN = {0016-2736},
      MRCLASS = {03C62},
      MRNUMBER = {4361589},
      DOI = {10.4064/fm928-1-2021},
      eprint = {1808.01270},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://wp.me/p5M0LV-1LS},
      }
    • J. D. Hamkins and H. W. Woodin, “Open class determinacy is preserved by forcing,” Mathematics ArXiv, p. 1–14, 2018.
      [Bibtex]
      @ARTICLE{HamkinsWoodin2018:Open-class-determinacy-is-preserved-by-forcing,
      author = {Joel David Hamkins and W. Hugh Woodin},
      title = {Open class determinacy is preserved by forcing},
      journal = {Mathematics ArXiv},
      year = {2018},
      volume = {},
      number = {},
      pages = {1--14},
      month = {},
      note = {Under review},
      abstract = {},
      eprint = {1806.11180},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      keywords = {under-review},
      source = {},
      doi = {},
      url = {http://wp.me/p5M0LV-1KF},
      }
    • [DOI] J. D. Hamkins and K. J. Williams, “The $\Sigma_1$-definable universal finite sequence,” Journal of Symbolic Logic, 2021.
      [Bibtex]
      @ARTICLE{HamkinsWilliams2021:The-universal-finite-sequence,
      author = {Joel David Hamkins and Kameryn J. Williams},
      title = {The $\Sigma_1$-definable universal finite sequence},
      journal = {Journal of Symbolic Logic},
      year = {2021},
      volume = {},
      number = {},
      pages = {},
      month = {},
      note = {},
      abstract = {},
      keywords = {},
      eprint = {1909.09100},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      source = {},
      doi = {10.1017/jsl.2020.59},
      }
    • [DOI] V. Gitman, J. D. Hamkins, and A. Karagila, “Kelley-Morse set theory does not prove the class Fodor theorem,” Fundamenta Mathematicae, vol. 254, iss. 2, p. 133–154, 2021.
      [Bibtex]
      @ARTICLE{GitmanHamkinsKaragila:KM-set-theory-does-not-prove-the-class-Fodor-theorem,
      author = {Victoria Gitman and Joel David Hamkins and Asaf Karagila},
      title = {Kelley-Morse set theory does not prove the class {F}odor theorem},
      journal = {Fundamenta Mathematicae},
      VOLUME = {254},
      YEAR = {2021},
      NUMBER = {2},
      PAGES = {133--154},
      ISSN = {0016-2736},
      MRCLASS = {03E70 (03E25 03E35)},
      MRNUMBER = {4241500},
      DOI = {10.4064/fm725-9-2020},
      keywords = {},
      eprint = {1904.04190},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      source = {},
      url = {http://wp.me/p5M0LV-1RD},
      }
    • [DOI] J. Brendle, W. Brian, and J. D. Hamkins, “The subseries number,” Fund. Math., vol. 247, iss. 1, p. 49–85, 2019.
      [Bibtex]
      @ARTICLE{BrendleBrianHamkins2019:The-subseries-number,
      AUTHOR = {Brendle, J\"{o}rg and Brian, Will and Hamkins, Joel David},
      TITLE = {The subseries number},
      JOURNAL = {Fund. Math.},
      FJOURNAL = {Fundamenta Mathematicae},
      VOLUME = {247},
      YEAR = {2019},
      NUMBER = {1},
      PAGES = {49--85},
      ISSN = {0016-2736},
      MRCLASS = {03E17 (03E35 40A05)},
      MRNUMBER = {3984279},
      DOI = {10.4064/fm667-11-2018},
      url = {http://jdh.hamkins.org/the-subseries-number},
      eprint = {1801.06206},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      }
    • J. D. Hamkins, Topics in Logic, , 2021, Book manuscript, 398 pages, in preparation.
      [Bibtex]
      @BOOK{Hamkins:Topics-in-logic,
      author = {Joel David Hamkins},
      editor = {},
      title = {{Topics in Logic}},
      publisher = {},
      year = {2021},
      volume = {},
      number = {},
      series = {},
      address = {},
      edition = {},
      month = {},
      note = {Book manuscript, 398 pages, in preparation},
      abstract = {},
      isbn = {},
      price = {},
      keywords = {book,inprep},
      source = {},
      }
    • J. D. Hamkins, Proof and the Art of Mathematics, MIT Press, 2020.
      [Bibtex]
      @BOOK{Hamkins2020:Proof-and-the-art-of-mathematics,
      author = {Joel David Hamkins},
      title = {Proof and the {Art} of {Mathematics}},
      publisher = {MIT Press},
      year = {2020},
      isbn = {978-0-262-53979-1},
      keywords = {book},
      url = {https://mitpress.mit.edu/books/proof-and-art-mathematics},
      }
    • J. D. Hamkins, Proof and the Art of Mathematics: Examples and Extensions, MIT Press, 2021.
      [Bibtex]
      @BOOK{Hamkins2021:Proof-and-the-art-examples,
      author = {Joel David Hamkins},
      title = {{Proof and the Art of Mathematics: Examples and Extensions}},
      publisher = {MIT Press},
      year = {2021},
      isbn = {9780262542203},
      keywords = {book},
      url = {https://mitpress.mit.edu/books/proof-and-art-mathematics-1},
      }
    • J. D. Hamkins and H. W. Woodin, “The universal finite set,” Mathematics ArXiv, p. 1–16, 2017.
      [Bibtex]
      @ARTICLE{HamkinsWoodin:The-universal-finite-set,
      author = {Joel David Hamkins and W. Hugh Woodin},
      title = {The universal finite set},
      journal = {Mathematics ArXiv},
      year = {2017},
      volume = {},
      number = {},
      pages = {1--16},
      month = {},
      note = {Manuscript under review},
      abstract = {},
      keywords = {under-review},
      source = {},
      doi = {},
      eprint = {1711.07952},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://jdh.hamkins.org/the-universal-finite-set},
      }
    • J. D. Hamkins, “The modal logic of arithmetic potentialism and the universal algorithm,” Mathematics ArXiv, p. 1–35, 2018.
      [Bibtex]
      @ARTICLE{Hamkins:The-modal-logic-of-arithmetic-potentialism,
      author = {Joel David Hamkins},
      title = {The modal logic of arithmetic potentialism and the universal algorithm},
      journal = {Mathematics ArXiv},
      year = {2018},
      volume = {},
      number = {},
      pages = {1--35},
      month = {},
      eprint = {1801.04599},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      note = {Under review},
      url = {http://wp.me/p5M0LV-1Dh},
      abstract = {},
      keywords = {under-review},
      source = {},
      doi = {},
      }
    • J. D. Hamkins and J. Reitz, “The set-theoretic universe $V$ is not necessarily a class-forcing extension of HOD,” Mathematics ArXiv, 2017.
      [Bibtex]
      @ARTICLE{HamkinsReitz:The-set-theoretic-universe-is-not-necessarily-a-forcing-extension-of-HOD,
      author = {Joel David Hamkins and Jonas Reitz},
      title = {The set-theoretic universe {$V$} is not necessarily a class-forcing extension of {HOD}},
      journal = {Mathematics ArXiv},
      year = {2017},
      volume = {},
      number = {},
      pages = {},
      month = {September},
      note = {Manuscript under review},
      abstract = {},
      keywords = {under-review},
      source = {},
      doi = {},
      eprint = {1709.06062},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://jdh.hamkins.org/the-universe-need-not-be-a-class-forcing-extension-of-hod},
      }
    • [DOI] N. Barton, A. E. Caicedo, G. Fuchs, J. D. Hamkins, J. Reitz, and R. Schindler, “Inner-model reflection principles,” Studia Logica, vol. 108, p. 573–595, 2020.
      [Bibtex]
      @ARTICLE{BartonCaicedoFuchsHamkinsReitzSchindler2020:Inner-model-reflection-principles,
      author = {Neil Barton and Andr\'es Eduardo Caicedo and Gunter Fuchs and Joel David Hamkins and Jonas Reitz and Ralf Schindler},
      title = {Inner-model reflection principles},
      journal = {Studia Logica},
      year = {2020},
      volume = {108},
      number = {},
      pages = {573--595},
      month = {},
      note = {},
      abstract = {},
      keywords = {},
      source = {},
      doi = {10.1007/s11225-019-09860-7},
      eprint = {1708.06669},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://jdh.hamkins.org/inner-model-reflection-principles},
      }
    • G. Fuchs and J. D. Hamkins, “The Bukovský-Dehornoy phenomenon for Boolean ultrapowers,” ArXiv e-prints, 2017.
      [Bibtex]
      @ARTICLE{FuchsHamkins:TheBukovskyDehornoyPhenomenonForBooleanUltrapowers,
      AUTHOR = {Gunter Fuchs and Joel David Hamkins},
      TITLE = {The {Bukovsk\'y-Dehornoy} phenomenon for {Boolean} ultrapowers},
      JOURNAL = {ArXiv e-prints},
      YEAR = {2017},
      volume = {},
      number = {},
      pages = {},
      month = {},
      note = {Under review},
      abstract = {},
      keywords = {under-review},
      source = {},
      eprint = {1707.06702},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://wp.me/p5M0LV-1zz},
      }
    • [DOI] V. Gitman, J. D. Hamkins, P. Holy, P. Schlicht, and K. Williams, “The exact strength of the class forcing theorem,” Journal of Symbolic Logic, vol. 85, iss. 3, p. 869–905, 2020.
      [Bibtex]
      @ARTICLE{GitmanHamkinsHolySchlichtWilliams2020:The-exact-strength-of-the-class-forcing-theorem,
      author = {Victoria Gitman and Joel David Hamkins and Peter Holy and Philipp Schlicht and Kameryn Williams},
      title = {The exact strength of the class forcing theorem},
      journal = {Journal of Symbolic Logic},
      publisher={Cambridge University Press},
      year = {2020},
      pages={869–905},
      volume={85},
      DOI={10.1017/jsl.2019.89},
      number={3},
      note = {},
      abstract = {},
      keywords = {},
      source = {},
      eprint = {1707.03700},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://wp.me/p5M0LV-1yp},
      }
    • F. G. Dorais and J. D. Hamkins, “When does every definable nonempty set have a definable element?,” Mathematical Logic Quarterly, vol. 65, iss. 4, pp. 407-411, 2019.
      [Bibtex]
      @ARTICLE{DoraisHamkins:When-does-every-definable-nonempty-set-have-a-definable-element,
      author = {Dorais, François G. and Hamkins, Joel David},
      title = {When does every definable nonempty set have a definable element?},
      journal = {Mathematical Logic Quarterly},
      volume = {65},
      number = {4},
      pages = {407-411},
      doi = {10.1002/malq.201700035},
      abstract = {Abstract The assertion that every definable set has a definable element is equivalent over ZF to the principle V=HOD, and indeed, we prove, so is the assertion merely that every Π2-definable set has an ordinal-definable element. Meanwhile, every model of ZFC has a forcing extension satisfying V≠HOD in which every Σ2-definable set has an ordinal-definable element. Similar results hold for HOD(R) and HOD(Ordω) and other natural instances of HOD(X).},
      year = {2019},
      keywords = {},
      source = {},
      doi = {},
      eprint = {1706.07285},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://jdh.hamkins.org/definable-sets-with-definable-elements},
      }
    • [DOI] V. Gitman and J. D. Hamkins, “A model of the generic Vopěnka principle in which the ordinals are not Mahlo,” Archive for Mathematical Logic, p. 1–21, 2018.
      [Bibtex]
      @ARTICLE{GitmanHamkins2018:A-model-of-the-generic-Vopenka-principle-in-which-the-ordinals-are-not-Mahlo,
      author = {Gitman, Victoria and Hamkins, Joel David},
      year = {2018},
      title = {A model of the generic Vopěnka principle in which the ordinals are not Mahlo},
      journal = {Archive for Mathematical Logic},
      issn = {0933-5846},
      doi = {10.1007/s00153-018-0632-5},
      month = {5},
      pages = {1--21},
      eprint = {1706.00843},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://wp.me/p5M0LV-1xT},
      abstract = {The generic Vopěnka principle, we prove, is relatively consistent with the ordinals being non-Mahlo. Similarly, the generic Vopěnka scheme is relatively consistent with the ordinals being definably non-Mahlo. Indeed, the generic Vopěnka scheme is relatively consistent with the existence of a Δ2-definable class containing no regular cardinals. In such a model, there can be no Σ2-reflecting cardinals and hence also no remarkable cardinals. This latter fact answers negatively a question of Bagaria, Gitman and Schindler.},
      }
    • J. D. Hamkins and M. Kikuchi, “The inclusion relations of the countable models of set theory are all isomorphic,” ArXiv e-prints, 2017.
      [Bibtex]
      @ARTICLE{HamkinsKikuchi:The-inclusion-relations-of-the-countable-models-of-set-theory-are-all-isomorphic,
      author = {Joel David Hamkins and Makoto Kikuchi},
      title = {The inclusion relations of the countable models of set theory are all isomorphic},
      journal = {ArXiv e-prints},
      editor = {},
      year = {2017},
      volume = {},
      number = {},
      pages = {},
      month = {},
      doi = {},
      note = {Manuscript under review},
      eprint = {1704.04480},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://jdh.hamkins.org/inclusion-relations-are-all-isomorphic},
      abstract = {},
      keywords = {under-review},
      source = {},
      }
    • [DOI] M. T. Godziszewski and J. D. Hamkins, “Computable Quotient Presentations of Models of Arithmetic and Set Theory,” in Logic, Language, Information, and Computation: 24th International Workshop, WoLLIC 2017, London, UK, July 18-21, 2017, Proceedings, J. Kennedy and R. J. G. B. de Queiroz, Eds., Springer, 2017, p. 140–152.
      [Bibtex]
      @Inbook{GodziszewskiHamkins2017:Computable-quotient-presentations-of-models-of-arithmetic-and-set-theory,
      author="Godziszewski, Micha{\l} Tomasz and Hamkins, Joel David",
      editor="Kennedy, Juliette and de Queiroz, Ruy J.G.B.",
      title="Computable Quotient Presentations of Models of Arithmetic and Set Theory",
      bookTitle="{Logic, Language, Information, and Computation: 24th International Workshop, WoLLIC 2017, London, UK, July 18-21, 2017, Proceedings}",
      year="2017",
      publisher="Springer",
      address="",
      pages="140--152",
      abstract="We prove various extensions of the Tennenbaum phenomenon to the case of computable quotient presentations of models of arithmetic and set theory. Specifically, no nonstandard model of arithmetic has a computable quotient presentation by a c.e. equivalence relation. No {\$}{\$}{\backslash}Sigma {\_}1{\$}{\$} -sound nonstandard model of arithmetic has a computable quotient presentation by a co-c.e. equivalence relation. No nonstandard model of arithmetic in the language {\$}{\$}{\backslash}{\{}+,{\backslash}cdot ,{\backslash}le {\backslash}{\}}{\$}{\$} has a computably enumerable quotient presentation by any equivalence relation of any complexity. No model of ZFC or even much weaker set theories has a computable quotient presentation by any equivalence relation of any complexity. And similarly no nonstandard model of finite set theory has a computable quotient presentation.",
      isbn="978-3-662-55386-2",
      doi="10.1007/978-3-662-55386-2_10",
      eprint = {1702.08350},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://wp.me/p5M0LV-1tW},
      }
    • [DOI] M. J. Groszek and J. D. Hamkins, “The implicitly constructible universe,” Journal of Symbolic Logic, vol. 84, iss. 4, p. 1403–1421, 2019.
      [Bibtex]
      @ARTICLE{GroszekHamkins2019:The-implicitly-constructible-universe,
      AUTHOR = {Groszek, Marcia J. and Hamkins, Joel David},
      TITLE = {The implicitly constructible universe},
      JOURNAL = {Journal of Symbolic Logic},
      FJOURNAL = {The Journal of Symbolic Logic},
      VOLUME = {84},
      YEAR = {2019},
      NUMBER = {4},
      PAGES = {1403--1421},
      ISSN = {0022-4812},
      MRCLASS = {03E35 (03E45)},
      MRNUMBER = {4045982},
      DOI = {10.1017/jsl.2018.57},
      eprint = {1702.07947},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://jdh.hamkins.org/the-implicitly-constructible-universe},
      }
    • [DOI] A. Enayat and J. D. Hamkins, “ZFC proves that the class of ordinals is not weakly compact for definable classes,” Journal of Symbolic Logic, vol. 83, iss. 1, p. 146–164, 2018.
      [Bibtex]
      @ARTICLE{EnayatHamkins2018:Ord-is-not-definably-weakly-compact,
      author = {Ali Enayat and Joel David Hamkins},
      title = {{ZFC} proves that the class of ordinals is not weakly compact for definable classes},
      journal = {Journal of Symbolic Logic},
      year = {2018},
      volume = {83},
      number = {1},
      pages = {146--164},
      month = {},
      note = {},
      abstract = {},
      keywords = {},
      source = {},
      doi = {10.1017/jsl.2017.75},
      eprint = {1610.02729},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://jdh.hamkins.org/ord-is-not-definably-weakly-compact},
      }
    • [DOI] J. D. Hamkins and O, “The modal logic of set-theoretic potentialism and the potentialist maximality principles,” Review of Symbolic Logic, vol. 15, iss. 1, p. 1–35, 2022.
      [Bibtex]
      @article {HamkinsLinnebo2022:Modal-logic-of-set-theoretic-potentialism,
      AUTHOR = {Joel David Hamkins and {\O}ystein Linnebo},
      TITLE = {The modal logic of set-theoretic potentialism and the potentialist maximality principles},
      JOURNAL = {Review of Symbolic Logic},
      VOLUME = {15},
      YEAR = {2022},
      NUMBER = {1},
      PAGES = {1--35},
      ISSN = {1755-0203},
      MRCLASS = {03Exx (03B45 03C62)},
      MRNUMBER = {4394758},
      DOI = {10.1017/S1755020318000242},
      eprint = {1708.01644},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://wp.me/p5M0LV-1zC},
      }
    • J. D. Hamkins, “The Vopěnka principle is inequivalent to but conservative over the Vopěnka scheme,” ArXiv e-prints, 2016.
      [Bibtex]
      @ARTICLE{Hamkins:The-Vopenka-principle-is-inequivalent-to-but-conservative-over-the-Vopenka-scheme,
      author = {Joel David Hamkins},
      title = {The {Vop\v{e}nka} principle is inequivalent to but conservative over the {Vop\v{e}nka} scheme},
      journal = {ArXiv e-prints},
      year = {2016},
      volume = {},
      number = {},
      pages = {},
      month = {},
      note = {Under review},
      abstract = {},
      keywords = {under-review},
      source = {},
      eprint = {1606.03778},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://wp.me/p5M0LV-1lV},
      }
    • [DOI] J. D. Hamkins and M. Kikuchi, “Set-theoretic mereology,” Logic and Logical Philosophy, Special issue “Mereology and beyond, part II”, vol. 25, iss. 3, p. 285–308, 2016.
      [Bibtex]
      @ARTICLE{HamkinsKikuchi2016:Set-theoreticMereology,
      author = {Joel David Hamkins and Makoto Kikuchi},
      title = {Set-theoretic mereology},
      journal = {Logic and Logical Philosophy, Special issue ``Mereology and beyond, part II''},
      editor = {A.~C.~Varzi and R.~Gruszczy{\'n}ski},
      year = {2016},
      volume = {25},
      number = {3},
      pages = {285--308},
      month = {},
      doi = {10.12775/LLP.2016.007},
      note = {},
      eprint = {1601.06593},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://jdh.hamkins.org/set-theoretic-mereology},
      abstract = {},
      keywords = {},
      source = {},
      ISSN = {1425-3305},
      MRCLASS = {03A05 (03E70)},
      MRNUMBER = {3546211},
      }
    • J. D. Hamkins, “Upward closure and amalgamation in the generic multiverse of a countable model of set theory,” RIMS Kyôkyûroku, p. 17–31, 2016.
      [Bibtex]
      @ARTICLE{Hamkins2016:UpwardClosureAndAmalgamationInTheGenericMultiverse,
      author = {Joel David Hamkins},
      title = {Upward closure and amalgamation in the generic multiverse of a countable model of set theory},
      journal = {RIMS {Ky\^oky\^uroku}},
      year = {2016},
      volume = {},
      number = {},
      pages = {17--31},
      month = {},
      newton = {ni15066},
      url = {http://wp.me/p5M0LV-1cv},
      eprint = {1511.01074},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      abstract = {},
      keywords = {},
      source = {},
      issn = {1880-2818},
      }
    • [DOI] A. Blass, J. Brendle, W. Brian, J. D. Hamkins, M. Hardy, and P. B. Larson, “The rearrangement number,” Trans. Amer. Math. Soc., vol. 373, iss. 1, p. 41–69, 2020.
      [Bibtex]
      @ARTICLE{BlassBrendleBrianHamkinsHardyLarson2020:TheRearrangementNumber,
      author = {Andreas Blass and Jörg Brendle and Will Brian and Joel David Hamkins and Michael Hardy and Paul B. Larson},
      title = {The rearrangement number},
      JOURNAL = {Trans. Amer. Math. Soc.},
      FJOURNAL = {Transactions of the American Mathematical Society},
      VOLUME = {373},
      YEAR = {2020},
      NUMBER = {1},
      PAGES = {41--69},
      ISSN = {0002-9947},
      MRCLASS = {03E17 (03E35 40A05)},
      MRNUMBER = {4042868},
      DOI = {10.1090/tran/7881},
      note = {},
      url = {http://jdh.hamkins.org/the-rearrangement-number},
      eprint = {1612.07830},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      abstract = {},
      keywords = {},
      source = {},
      }
    • V. Gitman and J. D. Hamkins, “Open determinacy for class games,” in Foundations of Mathematics, Logic at Harvard, Essays in Honor of Hugh Woodin’s 60th Birthday, A. E. Caicedo, J. Cummings, P. Koellner, and P. Larson, Eds., , 2016, Newton Institute preprint ni15064.
      [Bibtex]
      @INCOLLECTION{GitmanHamkins2016:OpenDeterminacyForClassGames,
      author = {Victoria Gitman and Joel David Hamkins},
      title = {Open determinacy for class games},
      booktitle = {{Foundations of Mathematics, Logic at Harvard, Essays in Honor of Hugh Woodin's 60th Birthday}},
      publisher = {},
      year = {2016},
      editor = {Andr\'es E. Caicedo and James Cummings and Peter Koellner and Paul Larson},
      volume = {},
      number = {},
      series = {AMS Contemporary Mathematics},
      type = {},
      chapter = {},
      pages = {},
      address = {},
      edition = {},
      month = {},
      note = {Newton Institute preprint ni15064},
      url = {http://wp.me/p5M0LV-1af},
      eprint = {1509.01099},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      abstract = {},
      keywords = {},
      }
    • C.~D.~A.~Evans, J. D. Hamkins, and N. L. Perlmutter, “A position in infinite chess with game value $\omega^4$,” Integers, vol. 17, p. Paper No.~G4, 22, 2017.
      [Bibtex]
      @ARTICLE{EvansHamkinsPerlmutter2017:APositionInInfiniteChessWithGameValueOmega^4,
      author = {C.~D.~A.~Evans and Joel David Hamkins and Norman Lewis Perlmutter},
      title = {A position in infinite chess with game value $\omega^4$},
      journal = {Integers},
      FJOURNAL = {Integers Electronic Journal of Combinatorial Number Theory},
      year = {2017},
      volume = {17},
      number = {},
      pages = {Paper No.~G4, 22},
      eprint = {1510.08155},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://wp.me/p5M0LV-1c5},
      month = {},
      note = {},
      abstract = {},
      keywords = {},
      source = {},
      newton = {ni15065},
      }
    • V. Gitman and J. D. Hamkins, “Kelley-Morse set theory and choice principles for classes,” , 2017.
      [Bibtex]
      @ARTICLE{GitmanHamkins:Kelley-MorseSetTheoryAndChoicePrinciplesForClasses,
      author = {Victoria Gitman and Joel David Hamkins},
      title = {{Kelley-Morse} set theory and choice principles for classes},
      journal = {},
      year = {2017},
      volume = {},
      number = {},
      pages = {},
      month = {},
      note = {Unpublished manuscript},
      abstract = {},
      keywords = {inprep},
      source = {},
      }
    • D. Asperó, J. D. Hamkins, Y. Hayut, M. Magidor, and W. Woodin, “On Embeddings of the universe into the constructible universe,” , 2014.
      [Bibtex]
      @ARTICLE{AsperoHamkinsHayutMagidorWoodin:OnEmbeddingsOfTheUniverseIntoTheConstructibleUniverse,
      author = {David Asper\'o and Joel David Hamkins and Yair Hayut and Menachem Magidor and W.~Hugh Woodin},
      title = {On Embeddings of the universe into the constructible universe},
      journal = {},
      year = {2014},
      volume = {},
      number = {},
      pages = {},
      month = {},
      note = {Manuscript in preparation},
      abstract = {},
      keywords = {inprep},
      source = {},
      }
    • M. Gitik and J. D. Hamkins, “Large cardinals necessarily large in HOD,” , 2014.
      [Bibtex]
      @ARTICLE{GitikHamkins:LargeCardinalsNecessarilyLargeInHOD,
      author = {Moti Gitik and Joel David Hamkins},
      title = {Large cardinals necessarily large in {HOD}},
      journal = {},
      year = {2014},
      volume = {},
      number = {},
      pages = {},
      month = {},
      note = {Manuscript in preparation},
      abstract = {},
      keywords = {noCV,inprep},
      source = {},
      }
    • J. D. Hamkins, Math for eight-year-olds: graph theory for kids, Hacker Newsletter, issue 248, April 17 , 2015.
      [Bibtex]
      @MISC{Hamkins2015:MathForEightYearOlds-GraphTheoryForKids,
      author = {Joel David Hamkins},
      title = {Math for eight-year-olds: graph theory for kids},
      howpublished = {Hacker Newsletter, issue 248, April 17},
      year = {2015},
      url = {http://us1.campaign-archive1.com/? u=faa8eb4ef3a111cef92c4f3d4&id=272a943c0b},
      note = {},
      abstract = {},
      keywords = {noCV},
      source = {},
      }
    • J. D. Hamkins, A Mathematician’s Year in Japan, Amazon Kindle Direct Publishing, 2015, 156 pages.
      [Bibtex]
      @BOOK{Hamkins2015:AMathematiciansYearInJapan,
      author = {Joel David Hamkins},
      title = {A {Mathematician's} {Year} in {Japan}},
      publisher = {Amazon Kindle Direct Publishing},
      year = {2015},
      month = {March},
      keywords = {book},
      url = {http://www.amazon.com/dp/B00U618LM2},
      note = {156 pages},
      }
    • [DOI] G. Fuchs, V. Gitman, and J. D. Hamkins, “Ehrenfeucht’s Lemma in Set Theory,” Notre Dame Journal of Formal Logic, vol. 59, iss. 3, p. 355–370, 2018.
      [Bibtex]
      @ARTICLE{FuchsGitmanHamkins2018:EhrenfeuchtsLemmaInSetTheory,
      author = "Fuchs, Gunter and Gitman, Victoria and Hamkins, Joel David",
      doi = "10.1215/00294527-2018-0007",
      fjournal = "Notre Dame Journal of Formal Logic",
      journal = "Notre Dame Journal of Formal Logic",
      number = "3",
      pages = "355--370",
      publisher = "Duke University Press",
      title = "Ehrenfeucht’s Lemma in Set Theory",
      volume = "59",
      year = "2018",
      eprint = {1501.01918},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://jdh.hamkins.org/ehrenfeuchts-lemma-in-set-theory},
      }
    • [DOI] G. Fuchs, V. Gitman, and J. D. Hamkins, “Incomparable $\omega_1$-like models of set theory,” Math.~Logic Q., p. 1–11, 2017.
      [Bibtex]
      @article {FuchsGitmanHamkins2017:IncomparableOmega1-likeModelsOfSetTheory,
      author = {Fuchs, Gunter and Gitman, Victoria and Hamkins, Joel David},
      title = {Incomparable $\omega_1$-like models of set theory},
      journal = {Math.~Logic Q.},
      issn = {1521-3870},
      doi = {10.1002/malq.201500002},
      pages = {1--11},
      year = {2017},
      month = {March},
      eprint = {1501.01022},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://jdh.hamkins.org/incomparable-omega-one-like-models-of-set-theory},
      }
    • [DOI] Y. Cheng, S. Friedman, and J. D. Hamkins, “Large cardinals need not be large in HOD,” Annals of Pure and Applied Logic, vol. 166, iss. 11, pp. 1186-1198, 2015.
      [Bibtex]
      @ARTICLE{ChengFriedmanHamkins2015:LargeCardinalsNeedNotBeLargeInHOD,
      title = "Large cardinals need not be large in {HOD} ",
      journal = "Annals of Pure and Applied Logic ",
      volume = "166",
      number = "11",
      pages = "1186 - 1198",
      year = "2015",
      note = "",
      issn = "0168-0072",
      doi = "10.1016/j.apal.2015.07.004",
      eprint = {1407.6335},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://jdh.hamkins.org/large-cardinals-need-not-be-large-in-hod},
      author = "Yong Cheng and Sy-David Friedman and Joel David Hamkins",
      keywords = "Large cardinals",
      keywords = "HOD",
      keywords = "Forcing",
      keywords = "Absoluteness ",
      abstract = "Abstract We prove that large cardinals need not generally exhibit their large cardinal nature in HOD. For example, a supercompact cardinal κ need not be weakly compact in HOD, and there can be a proper class of supercompact cardinals in V, none of them weakly compact in HOD, with no supercompact cardinals in HOD. Similar results hold for many other types of large cardinals, such as measurable and strong cardinals.",
      }
    • [DOI] J. D. Hamkins and T. Johnstone, “Strongly uplifting cardinals and the boldface resurrection axioms,” Archive for Mathematical Logic, vol. 56, iss. 7, p. 1115–1133, 2017.
      [Bibtex]
      @ARTICLE{HamkinsJohnstone2017:StronglyUpliftingCardinalsAndBoldfaceResurrection,
      author = {Joel David Hamkins and Thomas Johnstone},
      title = {Strongly uplifting cardinals and the boldface resurrection axioms},
      journal="Archive for Mathematical Logic",
      year="2017",
      month="Nov",
      day="01",
      volume="56",
      number="7",
      pages="1115--1133",
      eprint = {1403.2788},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      issn="1432-0665",
      doi="10.1007/s00153-017-0542-y",
      url = {http://wp.me/p5M0LV-IE},
      abstract="We introduce the strongly uplifting cardinals, which are equivalently characterized, we prove, as the superstrongly unfoldable cardinals and also as the almost-hugely unfoldable cardinals, and we show that their existence is equiconsistent over ZFC with natural instances of the boldface resurrection axiom, such as the boldface resurrection axiom for proper forcing.",
      keywords = {},
      source = {},
      }
    • J. D. Hamkins and R. Yang, “Satisfaction is not absolute,” to appear in the Review of Symbolic Logic, p. 1–34, 2014.
      [Bibtex]
      @ARTICLE{HamkinsYang:SatisfactionIsNotAbsolute,
      author = {Joel David Hamkins and Ruizhi Yang},
      title = {Satisfaction is not absolute},
      journal = {to appear in the Review of Symbolic Logic},
      year = {2014},
      volume = {},
      number = {},
      pages = {1--34},
      month = {},
      note = {},
      abstract = {},
      keywords = {to-appear},
      source = {},
      eprint = {1312.0670},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://wp.me/p5M0LV-Gf},
      doi = {},
      }
    • A. S. Daghighi, M. Golshani, J. Hamkins, and E. Jeřábek, “The foundation axiom and elementary self-embeddings of the universe,” in Infinity, Computability, and Metamathematics: Festschrift celebrating the 60th birthdays of Peter Koepke and Philip Welch, S. Geschke, B. Löwe, and P. Schlicht, Eds., College Publishers, 2014, vol. 23, p. 89–112.
      [Bibtex]
      @incollection {DaghighiGolshaniHaminsJerabek2013:TheFoundationAxiomAndElementarySelfEmbeddingsOfTheUniverse,
      AUTHOR = {Daghighi, Ali Sadegh and Golshani, Mohammad and Hamkins, Joel
      David and Je{\v{r}}{\'a}bek, Emil},
      TITLE = {The foundation axiom and elementary self-embeddings of the
      universe},
      BOOKTITLE = {{Infinity, Computability, and Metamathematics:
      Festschrift celebrating the 60th birthdays of Peter Koepke
      and Philip Welch}},
      SERIES = {Tributes},
      VOLUME = {23},
      PAGES = {89--112},
      PUBLISHER = {College Publishers},
      EDITOR = {S. Geschke and B. Löwe and P. Schlicht},
      YEAR = {2014},
      MRCLASS = {03E70 (03E30)},
      MRNUMBER = {3307881},
      eprint = {1311.0814},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://jdh.hamkins.org/the-role-of-foundation-in-the-kunen-inconsistency/},
      }
    • [DOI] J. D. Hamkins, “A multiverse perspective on the axiom of constructibility,” in Infinity and Truth, World Sci. Publ., Hackensack, NJ, 2014, vol. 25, p. 25–45.
      [Bibtex]
      @incollection {Hamkins2014:MultiverseOnVeqL,
      AUTHOR = {Hamkins, Joel David},
      TITLE = {A multiverse perspective on the axiom of constructibility},
      BOOKTITLE = {{Infinity and Truth}},
      SERIES = {LNS Math Natl. Univ. Singap.},
      VOLUME = {25},
      PAGES = {25--45},
      PUBLISHER = {World Sci. Publ., Hackensack, NJ},
      YEAR = {2014},
      MRCLASS = {03E45 (03A05)},
      MRNUMBER = {3205072},
      DOI = {10.1142/9789814571043_0002},
      url = {http://wp.me/p5M0LV-qE},
      eprint = {1210.6541},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      }
    • [DOI] J. D. Hamkins and T. Johnstone, “Resurrection axioms and uplifting cardinals,” Archive for Mathematical Logic, vol. 53, iss. 3-4, p. p.~463–485, 2014.
      [Bibtex]
      @ARTICLE{HamkinsJohnstone2014:ResurrectionAxiomsAndUpliftingCardinals,
      AUTHOR = "Joel David Hamkins and Thomas Johnstone",
      TITLE = "Resurrection axioms and uplifting cardinals",
      JOURNAL = "Archive for Mathematical Logic",
      publisher= {Springer},
      YEAR = "2014",
      volume = "53",
      number = "3-4",
      pages = "p.~463--485",
      month = "",
      note = "",
      url = "http://jdh.hamkins.org/resurrection-axioms-and-uplifting-cardinals",
      eprint = "1307.3602",
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      doi= "10.1007/s00153-014-0374-y",
      issn= {0933-5846},
      abstract = "",
      keywords = "",
      source = "",
      file = F,
      }
    • [DOI] J. Bagaria, J. D. Hamkins, K. Tsaprounis, and T. Usuba, “Superstrong and other large cardinals are never Laver indestructible,” Arch. Math. Logic, vol. 55, iss. 1-2, p. 19–35, 2016.
      [Bibtex]
      @ARTICLE{BagariaHamkinsTsaprounisUsuba2016:SuperstrongAndOtherLargeCardinalsAreNeverLaverIndestructible,
      AUTHOR = {Bagaria, Joan and Hamkins, Joel David and Tsaprounis,
      Konstantinos and Usuba, Toshimichi},
      TITLE = {Superstrong and other large cardinals are never {L}aver
      indestructible},
      JOURNAL = {Arch. Math. Logic},
      FJOURNAL = {Archive for Mathematical Logic},
      note = {Special volume in memory of R.~Laver},
      VOLUME = {55},
      YEAR = {2016},
      NUMBER = {1-2},
      PAGES = {19--35},
      ISSN = {0933-5846},
      MRCLASS = {03E55 (03E40)},
      MRNUMBER = {3453577},
      MRREVIEWER = {Peter Holy},
      DOI = {10.1007/s00153-015-0458-3},
      eprint = {1307.3486},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://jdh.hamkins.org/superstrong-never-indestructible/},
      }
    • [DOI] J. D. Hamkins and C. Leahy, “Algebraicity and Implicit Definability in Set Theory,” Notre Dame Journal of Formal Logic, vol. 57, iss. 3, p. 431–439, 2016.
      [Bibtex]
      @article{HamkinsLeahy2016:AlgebraicityAndImplicitDefinabilityInSetTheory,
      author = "Hamkins, Joel David and Leahy, Cole",
      doi = "10.1215/00294527-3542326",
      fjournal = "Notre Dame Journal of Formal Logic",
      journal = "Notre Dame Journal of Formal Logic",
      number = "3",
      pages = "431--439",
      publisher = "Duke University Press",
      title = "Algebraicity and Implicit Definability in Set Theory",
      volume = "57",
      year = "2016",
      url = {http://jdh.hamkins.org/algebraicity-and-implicit-definability},
      eprint = {1305.5953},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      ISSN = {0029-4527},
      MRCLASS = {03E47 (03C55)},
      MRNUMBER = {3521491},
      }
    • C.~D.~A.~Evans and J. D. Hamkins, “Transfinite game values in infinite chess,” Integers, vol. 14, p. Paper No.~G2, 36, 2014.
      [Bibtex]
      @ARTICLE{EvansHamkins2014:TransfiniteGameValuesInInfiniteChess,
      AUTHOR = {C.~D.~A.~Evans and Joel David Hamkins},
      TITLE = {Transfinite game values in infinite chess},
      JOURNAL = {Integers},
      FJOURNAL = {Integers Electronic Journal of Combinatorial Number Theory},
      YEAR = {2014},
      volume = {14},
      number = {},
      pages = {Paper No.~G2, 36},
      month = {},
      note = {},
      eprint = {1302.4377},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://jdh.hamkins.org/game-values-in-infinite-chess},
      ISSN = {1553-1732},
      MRCLASS = {03Exx (91A46)},
      MRNUMBER = {3225916},
      abstract = {},
      keywords = {},
      source = {},
      }
    • J. D. Hamkins and Z. Li, “Computable functionals on the countable ordinals,” , 2011.
      [Bibtex]
      @ARTICLE{HamkinsLi:ComputableFunctionalsOnTheCountableOrdinals,
      author = {Joel David Hamkins and Zhenhao Li},
      title = {Computable functionals on the countable ordinals},
      journal = {},
      year = {2011},
      volume = {},
      number = {},
      pages = {},
      month = {},
      note = {In preparation},
      abstract = {},
      keywords = {noCV,inprep},
      source = {},
      }
    • [DOI] B. Cody, M. Gitik, J. D. Hamkins, and J. A. Schanker, “The least weakly compact cardinal can be unfoldable, weakly measurable and nearly $\theta$ supercompact,” Archive for Mathematical Logic, p. 1–20, 2015.
      [Bibtex]
      @article{CodyGitikHamkinsSchanker2015:LeastWeaklyCompact,
      year= {2015},
      issn= {0933-5846},
      journal= {Archive for Mathematical Logic},
      doi= {10.1007/s00153-015-0423-1},
      title= {The least weakly compact cardinal can be unfoldable, weakly measurable and nearly $\theta$ supercompact},
      publisher= {Springer},
      keywords= {Weakly compact; Unfoldable; Weakly measurable; Nearly supercompact; Identity crisis; Primary 03E55; 03E35},
      author= {Cody, Brent and Gitik, Moti and Hamkins, Joel David and Schanker, Jason A.},
      pages= {1--20},
      language= {English},
      eprint = {1305.5961},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url= {http://jdh.hamkins.org/least-weakly-compact},
      }
    • J. D. Hamkins, “A question for the mathematics oracle,” to appear, p. 1.
      [Bibtex]
      @ARTICLE{Hamkins:AQuestionForTheMathematicsOracle,
      author = {Joel David Hamkins},
      title = {A question for the mathematics oracle},
      journal = {to appear},
      year = {},
      volume = {},
      number = {},
      pages = {1},
      month = {},
      note = {},
      abstract = {},
      keywords = {noCV},
      source = {},
      }
    • [DOI] J. D. Hamkins and B. Löwe, “Moving up and down in the generic multiverse,” Logic and its Applications, ICLA 2013 LNCS, vol. 7750, p. 139–147, 2013.
      [Bibtex]
      @ARTICLE{HamkinsLoewe2013:MovingUpAndDownInTheGenericMultiverse,
      AUTHOR = {Joel David Hamkins and Benedikt Löwe},
      title = {Moving up and down in the generic multiverse},
      journal = {Logic and its Applications, ICLA 2013 LNCS},
      publisher= {Springer},
      editor= {Lodaya, Kamal},
      isbn= {978-3-642-36038-1},
      year = {2013},
      volume = {7750},
      number = {},
      pages = {139--147},
      doi= {10.1007/978-3-642-36039-8_13},
      month = {},
      note = {},
      url = {http://wp.me/p5M0LV-od},
      eprint = {1208.5061},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      abstract = {},
      keywords = {},
      source = {},
      }
    • [DOI] J. D. Hamkins, G. Leibman, and B. Löwe, “Structural connections between a forcing class and its modal logic,” Israel Journal of Mathematics, vol. 207, iss. 2, p. 617–651, 2015.
      [Bibtex]
      @article {HamkinsLeibmanLoewe2015:StructuralConnectionsForcingClassAndItsModalLogic,
      AUTHOR = {Hamkins, Joel David and Leibman, George and Löwe,
      Benedikt},
      TITLE = {Structural connections between a forcing class and its modal
      logic},
      JOURNAL = {Israel Journal of Mathematics},
      FJOURNAL = {Israel Journal of Mathematics},
      VOLUME = {207},
      YEAR = {2015},
      NUMBER = {2},
      PAGES = {617--651},
      ISSN = {0021-2172},
      MRCLASS = {03E40 (03B45)},
      MRNUMBER = {3359713},
      DOI = {10.1007/s11856-015-1185-5},
      url = {http://wp.me/p5M0LV-kf},
      eprint = {1207.5841},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      }
    • [DOI] J. D. Hamkins, “Every countable model of set theory embeds into its own constructible universe,” Journal of Mathematical Logic, vol. 13, iss. 2, p. 1350006, 27, 2013.
      [Bibtex]
      @article {Hamkins2013:EveryCountableModelOfSetTheoryEmbedsIntoItsOwnL,
      AUTHOR = {Hamkins, Joel David},
      TITLE = {Every countable model of set theory embeds into its own
      constructible universe},
      JOURNAL = {Journal of Mathematical Logic},
      VOLUME = {13},
      YEAR = {2013},
      NUMBER = {2},
      PAGES = {1350006, 27},
      ISSN = {0219-0613},
      MRCLASS = {03C62 (03E99 05C20 05C60 05C63)},
      MRNUMBER = {3125902},
      MRREVIEWER = {Robert S. Lubarsky},
      DOI = {10.1142/S0219061313500062},
      eprint = {1207.0963},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      URL = {http://wp.me/p5M0LV-jn},
      }
    • [DOI] A. W. Apter, J. Cummings, and J. D. Hamkins, “Singular cardinals and strong extenders,” Central European Journal of Mathematics, vol. 11, iss. 9, p. 1628–1634, 2013.
      [Bibtex]
      @article {ApterCummingsHamkins2013:SingularCardinalsAndStrongExtenders,
      AUTHOR = {Apter, Arthur W. and Cummings, James and Hamkins, Joel David},
      TITLE = {Singular cardinals and strong extenders},
      JOURNAL = {Central European Journal of Mathematics},
      VOLUME = {11},
      YEAR = {2013},
      NUMBER = {9},
      PAGES = {1628--1634},
      ISSN = {1895-1074},
      MRCLASS = {03E55 (03E35 03E45)},
      MRNUMBER = {3071929},
      MRREVIEWER = {Samuel Gomes da Silva},
      DOI = {10.2478/s11533-013-0265-1},
      URL = {http://jdh.hamkins.org/singular-cardinals-strong-extenders/},
      eprint = {1206.3703},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      }
    • J. D. Hamkins and D. Seabold, “Well-founded Boolean ultrapowers as large cardinal embeddings,” , p. 1–40, 2006.
      [Bibtex]
      @ARTICLE{HamkinsSeabold:BooleanUltrapowers,
      AUTHOR = "Joel David Hamkins and Daniel Seabold",
      TITLE = "Well-founded {Boolean} ultrapowers as large cardinal embeddings",
      JOURNAL = "",
      YEAR = "2006",
      volume = "",
      number = "",
      pages = "1--40",
      month = "",
      note = "",
      eprint = "1206.6075",
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://jdh.hamkins.org/boolean-ultrapowers/},
      abstract = "",
      keywords = "",
      source = "",
      file = F,
      }
    • [DOI] J. D. Hamkins, “Is the dream solution of the continuum hypothesis attainable?,” Notre Dame Journal of Formal Logic, vol. 56, iss. 1, p. 135–145, 2015.
      [Bibtex]
      @article {Hamkins2015:IsTheDreamSolutionToTheContinuumHypothesisAttainable,
      AUTHOR = {Hamkins, Joel David},
      TITLE = {Is the dream solution of the continuum hypothesis attainable?},
      JOURNAL = {Notre Dame Journal of Formal Logic},
      FJOURNAL = {Notre Dame Journal of Formal Logic},
      VOLUME = {56},
      YEAR = {2015},
      NUMBER = {1},
      PAGES = {135--145},
      ISSN = {0029-4527},
      MRCLASS = {03E50},
      MRNUMBER = {3326592},
      MRREVIEWER = {Marek Balcerzak},
      DOI = {10.1215/00294527-2835047},
      eprint = {1203.4026},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://jdh.hamkins.org/dream-solution-of-ch},
      }
    • [DOI] V. Gitman, J. D. Hamkins, and T. A.~Johnstone, “What is the theory ZFC without Powerset?,” Math.~Logic Q., vol. 62, iss. 4–5, p. 391–406, 2016.
      [Bibtex]
      @ARTICLE{GitmanHamkinsJohnstone2016:WhatIsTheTheoryZFC-Powerset?,
      AUTHOR = {Victoria Gitman and Joel David Hamkins and Thomas A.~Johnstone},
      TITLE = {What is the theory {ZFC} without {Powerset}?},
      JOURNAL = {Math.~Logic Q.},
      YEAR = {2016},
      volume = {62},
      number = {4--5},
      pages = {391--406},
      month = {},
      note = {},
      abstract = {},
      keywords = {},
      doi = {10.1002/malq.201500019},
      eprint = {1110.2430},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://jdh.hamkins.org/what-is-the-theory-zfc-without-power-set},
      source = {},
      ISSN = {0942-5616},
      MRCLASS = {03E30},
      MRNUMBER = {3549557},
      MRREVIEWER = {Arnold W. Miller},
      }
    • [DOI] D. Brumleve, J. D. Hamkins, and P. Schlicht, “The Mate-in-$n$ Problem of Infinite Chess Is Decidable,” in How the World Computes, S. Cooper, A. Dawar, and B. Löwe, Eds., Springer, 2012, vol. 7318, pp. 78-88.
      [Bibtex]
      @incollection{BrumleveHamkinsSchlicht2012:TheMateInNProblemOfInfiniteChessIsDecidable,
      year= {2012},
      isbn= {978-3-642-30869-7},
      booktitle= {{How the World Computes}},
      volume= {7318},
      series= {Lecture Notes in Computer Science},
      editor= {Cooper, S.~Barry and Dawar, Anuj and Löwe, Benedikt},
      doi= {10.1007/978-3-642-30870-3_9},
      title= {The Mate-in-$n$ Problem of Infinite Chess Is Decidable},
      url= {http://wp.me/p5M0LV-f8},
      publisher= {Springer},
      author= {Brumleve, Dan and Hamkins, Joel David and Schlicht, Philipp},
      pages= {78-88},
      eprint = {1201.5597},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      }
    • [DOI] S. Coskey, J. D. Hamkins, and R. Miller, “The hierarchy of equivalence relations on the natural numbers under computable reducibility,” Computability, vol. 1, iss. 1, p. 15–38, 2012.
      [Bibtex]
      @ARTICLE{CoskeyHamkinsMiller2012:HierarchyOfEquivalenceRelationsOnN,
      AUTHOR = {Samuel Coskey and Joel David Hamkins and Russell Miller},
      TITLE = {The hierarchy of equivalence relations on the natural numbers under computable reducibility},
      JOURNAL = {Computability},
      YEAR = {2012},
      volume = {1},
      number = {1},
      pages = {15--38},
      month = {},
      note = {},
      url = {http://jdh.hamkins.org/equivalence-relations-on-naturals/},
      eprint = {1109.3375},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      doi = {10.3233/COM-2012-004},
      abstract = {},
      keywords = {},
      source = {},
      }
    • [DOI] G. Fuchs, J. D. Hamkins, and J. Reitz, “Set-theoretic geology,” Annals of Pure and Applied Logic, vol. 166, iss. 4, p. 464–501, 2015.
      [Bibtex]
      @article{FuchsHamkinsReitz2015:Set-theoreticGeology,
      author = "Gunter Fuchs and Joel David Hamkins and Jonas Reitz",
      title = "Set-theoretic geology",
      journal = "Annals of Pure and Applied Logic",
      volume = "166",
      number = "4",
      pages = "464--501",
      year = "2015",
      note = "",
      MRCLASS = {03E55 (03E40 03E45 03E47)},
      MRNUMBER = {3304634},
      issn = "0168-0072",
      doi = "10.1016/j.apal.2014.11.004",
      eprint = "1107.4776",
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = "http://jdh.hamkins.org/set-theoreticgeology",
      }
    • [DOI] J. D. Hamkins and J. Palumbo, “The rigid relation principle, a new weak choice principle,” Mathematical Logic Quarterly, vol. 58, iss. 6, p. 394–398, 2012.
      [Bibtex]
      @ARTICLE{HamkinsPalumbo2012:TheRigidRelationPrincipleANewWeakACPrinciple,
      AUTHOR = {Joel David Hamkins and Justin Palumbo},
      TITLE = {The rigid relation principle, a new weak choice principle},
      JOURNAL = {Mathematical Logic Quarterly},
      YEAR = {2012},
      volume = {58},
      number = {6},
      pages = {394--398},
      ISSN = {0942-5616},
      month = {},
      note = {},
      url = {http://jdh.hamkins.org/rigid-relation-principle/},
      eprint = {1106.4635},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      doi = {10.1002/malq.201100081},
      MRNUMBER = {2997028},
      MRREVIEWER = {Eleftherios C.~Tachtsis},
      abstract = {},
      keywords = {},
      source = {},
      }
    • [DOI] J. D. Hamkins, G. Kirmayer, and N. L. Perlmutter, “Generalizations of the Kunen inconsistency,” Annals of Pure and Applied Logic, vol. 163, iss. 12, pp. 1872-1890, 2012.
      [Bibtex]
      @article{HamkinsKirmayerPerlmutter2012:GeneralizationsOfKunenInconsistency,
      title = "Generalizations of the {Kunen} inconsistency",
      journal = "Annals of Pure and Applied Logic",
      volume = "163",
      number = "12",
      pages = "1872 - 1890",
      year = "2012",
      note = "",
      issn = "0168-0072",
      doi = "10.1016/j.apal.2012.06.001",
      eprint = {1106.1951},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = "http://jdh.hamkins.org/generalizationsofkuneninconsistency",
      author = "Joel David Hamkins and Greg Kirmayer and Norman Lewis Perlmutter",
      }
    • [DOI] J. D. Hamkins, D. Linetsky, and J. Reitz, “Pointwise definable models of set theory,” Journal of Symbolic Logic, vol. 78, iss. 1, p. 139–156, 2013.
      [Bibtex]
      @article {HamkinsLinetskyReitz2013:PointwiseDefinableModelsOfSetTheory,
      AUTHOR = {Hamkins, Joel David and Linetsky, David and Reitz, Jonas},
      TITLE = {Pointwise definable models of set theory},
      JOURNAL = {Journal of Symbolic Logic},
      FJOURNAL = {Journal of Symbolic Logic},
      VOLUME = {78},
      YEAR = {2013},
      NUMBER = {1},
      PAGES = {139--156},
      ISSN = {0022-4812},
      MRCLASS = {03E55},
      MRNUMBER = {3087066},
      MRREVIEWER = {Bernhard A. König},
      DOI = {10.2178/jsl.7801090},
      URL = {http://jdh.hamkins.org/pointwisedefinablemodelsofsettheory/},
      eprint = "1105.4597",
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      }
    • S. Coskey and J. D. Hamkins, “Infinite time Turing machines and an application to the hierarchy of equivalence relations on the reals,” in Effective Mathematics of the Uncountable, Assoc. Symbol. Logic, La Jolla, CA, 2013, vol. 41, p. 33–49.
      [Bibtex]
      @incollection {CoskeyHamkins2013:ITTMandApplicationsToEquivRelations,
      AUTHOR = {Coskey, Samuel and Hamkins, Joel David},
      TITLE = {Infinite time {T}uring machines and an application to the
      hierarchy of equivalence relations on the reals},
      BOOKTITLE = {{Effective Mathematics of the Uncountable}},
      SERIES = {Lect. Notes Log.},
      VOLUME = {41},
      PAGES = {33--49},
      PUBLISHER = {Assoc. Symbol. Logic, La Jolla, CA},
      YEAR = {2013},
      MRCLASS = {03D30 (03D60 03E15)},
      MRNUMBER = {3205053},
      eprint = {1101.1864},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://jdh.hamkins.org/ittms-and-applications/},
      }
    • [DOI] A. W.~Apter, V. Gitman, and J. D. Hamkins, “Inner models with large cardinal features usually obtained by forcing,” Archive for Math.~Logic, vol. 51, p. 257–283, 2012.
      [Bibtex]
      @article {ApterGitmanHamkins2012:InnerModelsWithLargeCardinals,
      author = {Arthur W.~Apter and Victoria Gitman and Joel David Hamkins},
      affiliation = {Mathematics, The Graduate Center of the City University of New York, 365 Fifth Avenue, New York, NY 10016, USA},
      title = {Inner models with large cardinal features usually obtained by forcing},
      journal = {Archive for Math.~Logic},
      publisher = {Springer},
      issn = {0933-5846},
      keyword = {},
      pages = {257--283},
      volume = {51},
      issue = {3},
      url = {http://jdh.hamkins.org/innermodels},
      eprint = {1111.0856},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      doi = {10.1007/s00153-011-0264-5},
      note = {},
      year = {2012},
      }
    • [DOI] J. D. Hamkins, “The set-theoretic multiverse,” Review of Symbolic Logic, vol. 5, p. 416–449, 2012.
      [Bibtex]
      @ARTICLE{Hamkins2012:TheSet-TheoreticalMultiverse,
      AUTHOR = {Joel David Hamkins},
      TITLE = {The set-theoretic multiverse},
      JOURNAL = {Review of Symbolic Logic},
      YEAR = {2012},
      volume = {5},
      number = {},
      pages = {416--449},
      month = {},
      note = {},
      url = {http://jdh.hamkins.org/themultiverse},
      doi = {10.1017/S1755020311000359},
      abstract = {},
      keywords = {},
      source = {},
      eprint = {1108.4223},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      }
    • [DOI] J. D. Hamkins, “Pointwise definable models of set theory, extended abstract,” Mathematisches Forschungsinstitut Oberwolfach Report, vol. 8, iss. 1, 02/2011, p. 128–131, 2011.
      [Bibtex]
      @ARTICLE{Hamkins2011:PointwiseDefinableModelsOfSetTheoryExtendedAbstract,
      AUTHOR = "Joel David Hamkins",
      TITLE = "Pointwise definable models of set theory, extended abstract",
      JOURNAL = "Mathematisches Forschungsinstitut Oberwolfach Report",
      YEAR = "2011",
      volume = "8",
      number = "1, 02/2011",
      pages = "128--131",
      month = "",
      note = "",
      abstract = "",
      keywords = "",
      source = "",
      DOI = {10.4171/OWR/2011/02},
      URL = {http://wp.me/p5M0LV-4n},
      file = F,
      }
    • Effective Mathematics of the Uncountable, N.~Greenberg, J.~D.~Hamkins, D.~R.~Hirschfeldt, and R.~G.~Miller, Eds., Cambridge University Press, ASL Lecture Notes in Logic, 2013, vol. 41.
      [Bibtex]
      @BOOK{EMU,
      AUTHOR = {},
      editor = {N.~Greenberg and J.~D.~Hamkins and D.~R.~Hirschfeldt and R.~G.~Miller},
      TITLE = {{Effective Mathematics of the Uncountable}},
      PUBLISHER = {Cambridge University Press, ASL Lecture Notes in Logic},
      YEAR = {2013},
      volume = {41},
      number = {},
      series = {},
      address = {},
      edition = {},
      month = {},
      note = {},
      abstract = {},
      isbn = {9781107014510},
      price = {},
      keywords = {book,edited-volume},
      url = {http://wp.me/s5M0LV-emu},
      source = {},
      }
    • [DOI] S. Coskey and J. D. Hamkins, “Infinite time decidable equivalence relation theory,” Notre Dame Journal of Formal Logic, vol. 52, iss. 2, p. 203–228, 2011.
      [Bibtex]
      @ARTICLE{CoskeyHamkins2011:InfiniteTimeComputableEquivalenceRelations,
      AUTHOR = {Coskey, Samuel and Hamkins, Joel David},
      TITLE = {Infinite time decidable equivalence relation theory},
      JOURNAL = {Notre Dame Journal of Formal Logic},
      FJOURNAL = {Notre Dame Journal of Formal Logic},
      VOLUME = {52},
      YEAR = {2011},
      NUMBER = {2},
      PAGES = {203--228},
      ISSN = {0029-4527},
      MRCLASS = {03D65 (03D30 03E15)},
      MRNUMBER = {2794652},
      DOI = {10.1215/00294527-1306199},
      URL = {http://wp.me/p5M0LV-3M},
      eprint = "0910.4616",
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      }
    • [DOI] J. D. Hamkins, “The Set-theoretic Multiverse : A Natural Context for Set Theory,” Annals of the Japan Association for Philosophy of Science, vol. 19, p. 37–55, 2011.
      [Bibtex]
      @article{Hamkins2011:TheMultiverse:ANaturalContext,
      author="Joel David Hamkins",
      title="The Set-theoretic Multiverse : A Natural Context for Set Theory",
      journal="Annals of the Japan Association for Philosophy of Science",
      ISSN="0453-0691",
      publisher="the Japan Association for Philosophy of Science",
      year="2011",
      volume="19",
      number="",
      pages="37--55",
      URL="http://jdh.hamkins.org/themultiverseanaturalcontext",
      doi={10.4288/jafpos.19.0_37},
      }
    • [DOI] V. Gitman and J. D. Hamkins, “A natural model of the multiverse axioms,” Notre Dame Journal of Formal Logic, vol. 51, iss. 4, p. 475–484, 2010.
      [Bibtex]
      @ARTICLE{GitmanHamkins2010:NaturalModelOfMultiverseAxioms,
      AUTHOR = {Gitman, Victoria and Hamkins, Joel David},
      TITLE = {A natural model of the multiverse axioms},
      JOURNAL = {Notre Dame Journal of Formal Logic},
      FJOURNAL = {Notre Dame Journal of Formal Logic},
      VOLUME = {51},
      YEAR = {2010},
      NUMBER = {4},
      PAGES = {475--484},
      ISSN = {0029-4527},
      MRCLASS = {03E40},
      MRNUMBER = {2741838},
      DOI = {10.1215/00294527-2010-030},
      URL = {http://wp.me/p5M0LV-3I},
      eprint = {1104.4450},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      }
    • [DOI] J. D. Hamkins and T. A. Johnstone, “Indestructible strong unfoldability,” Notre Dame Journal of Formal Logic, vol. 51, iss. 3, p. 291–321, 2010.
      [Bibtex]
      @ARTICLE{HamkinsJohnstone2010:IndestructibleStrongUnfoldability,
      AUTHOR = {Hamkins, Joel David and Johnstone, Thomas A.},
      TITLE = {Indestructible strong unfoldability},
      JOURNAL = {Notre Dame Journal of Formal Logic},
      FJOURNAL = {Notre Dame Journal of Formal Logic},
      VOLUME = {51},
      YEAR = {2010},
      NUMBER = {3},
      PAGES = {291--321},
      ISSN = {0029-4527},
      MRCLASS = {03E55 (03E40)},
      MRNUMBER = {2675684 (2011i:03050)},
      MRREVIEWER = {Bernhard A. König},
      DOI = {10.1215/00294527-2010-018},
      URL = {http://jdh.hamkins.org/indestructiblestrongunfoldability/},
      file = F,
      }
    • [DOI] J. D. Hamkins, “Some second order set theory,” in Logic and its Applications, R.~Ramanujam and S.~Sarukkai, Eds., Springer, 2009, vol. 5378, p. 36–50.
      [Bibtex]
      @INCOLLECTION{Hamkins2009:SomeSecondOrderSetTheory,
      AUTHOR = {Hamkins, Joel David},
      TITLE = {Some second order set theory},
      BOOKTITLE = {{Logic and its Applications}},
      SERIES = {Lecture Notes in Comput.~Sci.},
      VOLUME = {5378},
      PAGES = {36--50},
      PUBLISHER = {Springer},
      EDITOR = {R.~Ramanujam and S.~Sarukkai},
      ADDRESS = {},
      YEAR = {2009},
      MRCLASS = {03E35 (03B45 03E40)},
      MRNUMBER = {2540935 (2011a:03053)},
      DOI = {10.1007/978-3-540-92701-3_3},
      URL = {http://wp.me/p5M0LV-3E},
      }
    • [DOI] J. D. Hamkins and R. G. Miller, “Post’s problem for ordinal register machines: an explicit approach,” Ann.~Pure Appl.~Logic, vol. 160, iss. 3, p. 302–309, 2009.
      [Bibtex]
      @ARTICLE{HamkinsMiller2009:PostsProblemForORMsExplicitApproach,
      AUTHOR = {Hamkins, Joel David and Miller, Russell G.},
      TITLE = {Post's problem for ordinal register machines: an explicit approach},
      JOURNAL = {Ann.~Pure Appl.~Logic},
      FJOURNAL = {Annals of Pure and Applied Logic},
      VOLUME = {160},
      YEAR = {2009},
      NUMBER = {3},
      PAGES = {302--309},
      ISSN = {0168-0072},
      CODEN = {APALD7},
      MRCLASS = {03D60 (03D10)},
      MRNUMBER = {2555781 (2010m:03086)},
      MRREVIEWER = {Robert S.~Lubarsky},
      DOI = {10.1016/j.apal.2009.01.004},
      URL = {http://wp.me/p5M0LV-3C},
      file = F,
      }
    • [DOI] G. Fuchs and J. D. Hamkins, “Degrees of rigidity for Souslin trees,” Journal of Symbolic Logic, vol. 74, iss. 2, p. 423–454, 2009.
      [Bibtex]
      @ARTICLE{FuchsHamkins2009:DegreesOfRigidity,
      AUTHOR = {Fuchs, Gunter and Hamkins, Joel David},
      TITLE = {Degrees of rigidity for {S}ouslin trees},
      JOURNAL = {Journal of Symbolic Logic},
      FJOURNAL = {Journal of Symbolic Logic},
      VOLUME = {74},
      YEAR = {2009},
      NUMBER = {2},
      PAGES = {423--454},
      ISSN = {0022-4812},
      CODEN = {JSYLA6},
      MRCLASS = {03E05},
      MRNUMBER = {2518565 (2010i:03049)},
      MRREVIEWER = {Stefan Geschke},
      URL = {http://wp.me/p5M0LV-3A},
      doi = {10.2178/jsl/1243948321},
      eprint = {math/0602482},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      file = F,
      }
    • [DOI] J. D. Hamkins, “Tall cardinals,” Math.~Logic Q., vol. 55, iss. 1, p. 68–86, 2009.
      [Bibtex]
      @ARTICLE{Hamkins2009:TallCardinals,
      AUTHOR = {Hamkins, Joel D.},
      TITLE = {Tall cardinals},
      JOURNAL = {Math.~Logic Q.},
      FJOURNAL = {Mathematical Logic Quarterly},
      VOLUME = {55},
      YEAR = {2009},
      NUMBER = {1},
      PAGES = {68--86},
      ISSN = {0942-5616},
      MRCLASS = {03E55 (03E35)},
      MRNUMBER = {2489293 (2010g:03083)},
      MRREVIEWER = {Carlos A.~Di Prisco},
      DOI = {10.1002/malq.200710084},
      URL = {http://wp.me/p5M0LV-3y},
      file = F,
      }
    • [DOI] J. D. Hamkins and T. A. Johnstone, “The proper and semi-proper forcing axioms for forcing notions that preserve $\aleph_2$ or $\aleph_3$,” Proc.~Amer.~Math.~Soc., vol. 137, iss. 5, p. 1823–1833, 2009.
      [Bibtex]
      @ARTICLE{HamkinsJohnstone2009:PFA(aleph_2-preserving),
      AUTHOR = {Hamkins, Joel David and Johnstone, Thomas A.},
      TITLE = {The proper and semi-proper forcing axioms for forcing notions that preserve {$\aleph_2$} or {$\aleph_3$}},
      JOURNAL = {Proc.~Amer.~Math.~Soc.},
      FJOURNAL = {Proceedings of the American Mathematical Society},
      VOLUME = {137},
      YEAR = {2009},
      NUMBER = {5},
      PAGES = {1823--1833},
      ISSN = {0002-9939},
      CODEN = {PAMYAR},
      MRCLASS = {03E55 (03E40)},
      MRNUMBER = {2470843 (2009k:03087)},
      MRREVIEWER = {John Krueger},
      DOI = {10.1090/S0002-9939-08-09727-X},
      URL = {http://wp.me/p5M0LV-3v},
      file = F,
      }
    • J. D. Hamkins, R. Miller, D. Seabold, and S. Warner, “Infinite time computable model theory,” in New Computational Paradigms: Changing Conceptions of What is Computable, S. B. Cooper, B. Löwe, and A. Sorbi, Eds., Springer, 2008, p. 521–557.
      [Bibtex]
      @INCOLLECTION{HamkinsMillerSeaboldWarner2007:InfiniteTimeComputableModelTheory,
      AUTHOR = {Hamkins, Joel David and Miller, Russell and Seabold, Daniel
      and Warner, Steve},
      TITLE = {Infinite time computable model theory},
      BOOKTITLE = "{New Computational Paradigms: Changing Conceptions of What is Computable}",
      PAGES = {521--557},
      PUBLISHER = {Springer},
      ADDRESS = {},
      YEAR = {2008},
      MRCLASS = {03C57 (03D10)},
      MRNUMBER = {2762096},
      editor = {S. B. Cooper and Benedikt Löwe and Andrea Sorbi},
      isbn = "0-387-36033-6",
      file = F,
      url = {http://wp.me/p5M0LV-3t},
      }
    • [DOI] G. Fuchs and J. D. Hamkins, “Changing the heights of automorphism towers by forcing with Souslin trees over $L$,” Journal of Symbolic Logic, vol. 73, iss. 2, p. 614–633, 2008.
      [Bibtex]
      @ARTICLE{FuchsHamkins2008:ChangingHeightsOverL,
      AUTHOR = {Fuchs, Gunter and Hamkins, Joel David},
      TITLE = {Changing the heights of automorphism towers by forcing with {S}ouslin trees over {$L$}},
      JOURNAL = {Journal of Symbolic Logic},
      VOLUME = {73},
      YEAR = {2008},
      NUMBER = {2},
      PAGES = {614--633},
      ISSN = {0022-4812},
      CODEN = {JSYLA6},
      MRCLASS = {03E35},
      MRNUMBER = {2414468 (2009e:03094)},
      MRREVIEWER = {Lutz Struengmann},
      URL = {http://wp.me/p5M0LV-3l},
      doi = {10.2178/jsl/1208359063},
      eprint = {math/0702768},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      file = F,
      }
    • [DOI] J. D. Hamkins, J. Reitz, and W. Woodin, “The ground axiom is consistent with $V\ne{\rm HOD}$,” Proc.~Amer.~Math.~Soc., vol. 136, iss. 8, p. 2943–2949, 2008.
      [Bibtex]
      @ARTICLE{HamkinsReitzWoodin2008:TheGroundAxiomAndVequalsHOD,
      AUTHOR = {Hamkins, Joel David and Reitz, Jonas and Woodin, W.~Hugh},
      TITLE = {The ground axiom is consistent with {$V\ne{\rm HOD}$}},
      JOURNAL = {Proc.~Amer.~Math.~Soc.},
      FJOURNAL = {Proceedings of the American Mathematical Society},
      VOLUME = {136},
      YEAR = {2008},
      NUMBER = {8},
      PAGES = {2943--2949},
      ISSN = {0002-9939},
      CODEN = {PAMYAR},
      MRCLASS = {03E35 (03E45 03E55)},
      MRNUMBER = {2399062 (2009b:03137)},
      MRREVIEWER = {P{\'e}ter Komj{\'a}th},
      DOI = {10.1090/S0002-9939-08-09285-X},
      URL = {http://wp.me/p5M0LV-3j},
      file = F,
      }
    • [DOI] J. D. Hamkins and B. Löwe, “The modal logic of forcing,” Trans.~AMS, vol. 360, iss. 4, p. 1793–1817, 2008.
      [Bibtex]
      @ARTICLE{HamkinsLoewe2008:TheModalLogicOfForcing,
      AUTHOR = {Hamkins, Joel David and Löwe, Benedikt},
      TITLE = {The modal logic of forcing},
      JOURNAL = {Trans.~AMS},
      FJOURNAL = {Transactions of the American Mathematical Society},
      VOLUME = {360},
      YEAR = {2008},
      NUMBER = {4},
      PAGES = {1793--1817},
      ISSN = {0002-9947},
      CODEN = {TAMTAM},
      MRCLASS = {03E40 (03B45)},
      MRNUMBER = {2366963 (2009h:03068)},
      MRREVIEWER = {Andreas Blass},
      DOI = {10.1090/S0002-9947-07-04297-3},
      URL = {http://wp.me/p5M0LV-3h},
      eprint = {math/0509616},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      }
    • [DOI] A. W.~Apter, J. Cummings, and J. D. Hamkins, “Large cardinals with few measures,” Proc.~Amer.~Math.~Soc., vol. 135, iss. 7, p. 2291–2300, 2007.
      [Bibtex]
      @ARTICLE{ApterCummingsHamkins2006:LargeCardinalsWithFewMeasures,
      AUTHOR = {Arthur W.~Apter and James Cummings and Joel David Hamkins},
      TITLE = {Large cardinals with few measures},
      JOURNAL = {Proc.~Amer.~Math.~Soc.},
      FJOURNAL = {Proceedings of the American Mathematical Society},
      VOLUME = {135},
      YEAR = {2007},
      NUMBER = {7},
      PAGES = {2291--2300},
      ISSN = {0002-9939},
      CODEN = {PAMYAR},
      MRCLASS = {03E35 (03E55)},
      MRNUMBER = {2299507 (2008b:03067)},
      MRREVIEWER = {Tetsuya Ishiu},
      DOI = {10.1090/S0002-9939-07-08786-2},
      URL = {http://jdh.hamkins.org/largecardinalswithfewmeasures/},
      eprint = {math/0603260},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      file = F,
      }
    • [DOI] J. D. Hamkins, “A Survey of Infinite Time Turing Machines,” in Machines, Computations, and Universality – 5th International Conference MCU 2007, Orleans, France, 2007, p. 62–71.
      [Bibtex]
      @INPROCEEDINGS{Hamkins2007:ASurveyOfInfiniteTimeTuringMachines,
      AUTHOR = "Joel David Hamkins",
      TITLE = "A Survey of Infinite Time {T}uring Machines",
      BOOKTITLE = "{Machines, Computations, and Universality - 5th International Conference MCU 2007}",
      YEAR = "2007",
      editor = "{J\'er\^ ome} Durand-Lose and Maurice Margenstern",
      volume = "4664",
      number = "",
      series = "Lecture Notes in Computer Science",
      pages = "62--71",
      address = "Orleans, France",
      month = "",
      organization = "",
      publisher = "",
      note = "",
      abstract = "",
      keywords = "",
      doi = {10.1007/978-3-540-74593-8_5},
      file = F,
      url = {http://wp.me/p5M0LV-3d},
      }
    • [DOI] J. D. Hamkins, D. Linetsky, and R. Miller, “The Complexity of Quickly Decidable ORM-Decidable Sets,” in Computation and Logic in the Real World – CiE 2007, Siena, Italy, 2007, p. 488–496.
      [Bibtex]
      @INPROCEEDINGS{HamkinsLinetskyMiller2007:ComplexityOfQuicklyDecidableORMSets,
      AUTHOR = "Joel David Hamkins and David Linetsky and Russell Miller",
      TITLE = "The Complexity of Quickly Decidable {ORM}-Decidable Sets",
      BOOKTITLE = "{Computation and Logic in the Real World - CiE 2007}",
      YEAR = "2007",
      editor = "B. Cooper and B. Löwe and A.~Sorbi",
      volume = "4497",
      number = "",
      series = "Proc.~LNCS",
      pages = "488--496",
      address = "Siena, Italy",
      month = "",
      organization = "",
      publisher = "",
      note = "",
      abstract = "",
      keywords = "",
      doi = {10.1007/978-3-540-73001-9_51},
      ee = {},
      bibsource = {DBLP, http://dblp.uni-trier.de},
      file = F,
      url = {http://wp.me/p5M0LV-3b},
      }
    • [DOI] J. D. Hamkins and R. Miller, “Post’s Problem for Ordinal Register Machines,” in Computation and Logic in the Real World–-CiE 2007, Siena, Italy, 2007, pp. 358-367.
      [Bibtex]
      @INPROCEEDINGS{HamkinsMiller2007:PostsProblemForORMs,
      AUTHOR = "Joel David Hamkins and Russell Miller",
      TITLE = "Post's Problem for Ordinal Register Machines",
      BOOKTITLE = "{Computation and Logic in the Real World---CiE 2007}",
      YEAR = "2007",
      editor = "B. Cooper and B. Löwe and A.~Sorbi",
      volume = "4497",
      number = "",
      series = "Proc. LNCS",
      address = "Siena, Italy",
      month = "",
      organization = "",
      publisher = "",
      note = "",
      abstract = "",
      keywords = "",
      pages = {358-367},
      doi = {10.1007/978-3-540-73001-9_37},
      ee = {},
      file = F,
      url = {http://wp.me/p5M0LV-39},
      }
    • [DOI] J. D. Hamkins and A. Miasnikov, “The halting problem is decidable on a set of asymptotic probability one,” Notre Dame Journal of Formal Logic, vol. 47, iss. 4, p. 515–524, 2006.
      [Bibtex]
      @ARTICLE{HamkinsMiasnikov2006:HaltingProblemDecidable,
      AUTHOR = {Hamkins, Joel David and Miasnikov, Alexei},
      TITLE = {The halting problem is decidable on a set of asymptotic probability one},
      JOURNAL = {Notre Dame Journal of Formal Logic},
      VOLUME = {47},
      YEAR = {2006},
      NUMBER = {4},
      PAGES = {515--524},
      ISSN = {0029-4527},
      CODEN = {NDJFAM},
      MRCLASS = {03D10 (68Q05)},
      MRNUMBER = {2272085 (2007m:03082)},
      MRREVIEWER = {Maurice Margenstern},
      DOI = {10.1305/ndjfl/1168352664},
      URL = {http://jdh.hamkins.org/haltingproblemdecidable/},
      eprint = {math/0504351},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      }
    • [DOI] M. D{u{z}}amonja and J. D. Hamkins, “Diamond (on the regulars) can fail at any strongly unfoldable cardinal,” Ann.~Pure Appl.~Logic, vol. 144, iss. 1-3, p. 83–95, 2006.
      [Bibtex]
      @ARTICLE{DzamonjaHamkins2006:DiamondCanFail,
      AUTHOR = {D{\u{z}}amonja, Mirna and Hamkins, Joel David},
      TITLE = {Diamond (on the regulars) can fail at any strongly unfoldable cardinal},
      JOURNAL = {Ann.~Pure Appl.~Logic},
      FJOURNAL = {Annals of Pure and Applied Logic},
      VOLUME = {144},
      YEAR = {2006},
      NUMBER = {1-3},
      PAGES = {83--95},
      ISSN = {0168-0072},
      CODEN = {APALD7},
      MRCLASS = {03E05 (03E35 03E55)},
      MRNUMBER = {2279655 (2007m:03091)},
      MRREVIEWER = {Andrzej Ros{\l}anowski},
      DOI = {10.1016/j.apal.2006.05.001},
      URL = {http://jdh.hamkins.org/diamondcanfail/},
      month = {December},
      note = {Conference in honor of sixtieth birthday of James E.~Baumgartner},
      eprint = {math/0409304},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      }
    • [DOI] V. Deolalikar, J. D. Hamkins, and R. Schindler, “P $\neq$ NP $\cap$ co-NP for infinite time Turing machines,” Journal of Logic and Computation, vol. 15, iss. 5, p. 577–592, 2005.
      [Bibtex]
      @ARTICLE{DeolalikarHamkinsSchindler2005:NPcoNP,
      AUTHOR = {Deolalikar, Vinay and Hamkins, Joel David and Schindler, Ralf},
      TITLE = {P $\neq$ NP $\cap$ co-NP for infinite time {T}uring machines},
      JOURNAL = {Journal of Logic and Computation},
      VOLUME = {15},
      YEAR = {2005},
      NUMBER = {5},
      PAGES = {577--592},
      ISSN = {0955-792X},
      MRCLASS = {68Q05 (03D05 68Q15)},
      MRNUMBER = {2172411 (2006k:68026)},
      MRREVIEWER = {Peter G.~Hinman},
      DOI = {10.1093/logcom/exi022},
      URL = {http://jdh.hamkins.org/np-conp/},
      month = "October",
      eprint = {math/0307388},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      file = F,
      }
    • [DOI] J. D. Hamkins and W. Woodin, “The necessary maximality principle for c.c.c.~forcing is equiconsistent with a weakly compact cardinal,” Math.~Logic Q., vol. 51, iss. 5, p. 493–498, 2005.
      [Bibtex]
      @ARTICLE{HamkinsWoodin2005:NMPccc,
      AUTHOR = {Joel David Hamkins and W.~Hugh Woodin},
      TITLE = {The necessary maximality principle for c.c.c.~forcing is equiconsistent with a weakly compact cardinal},
      JOURNAL = {Math.~Logic Q.},
      FJOURNAL = {Mathematical Logic Quarterly},
      VOLUME = {51},
      YEAR = {2005},
      NUMBER = {5},
      PAGES = {493--498},
      ISSN = {0942-5616},
      MRCLASS = {03E65 (03E55)},
      MRNUMBER = {2163760 (2006f:03082)},
      MRREVIEWER = {Tetsuya Ishiu},
      DOI = {10.1002/malq.200410045},
      URL = {http://wp.me/s5M0LV-nmpccc},
      eprint = {math/0403165},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      file = F,
      }
    • J. D. Hamkins, “The Ground Axiom,” Mathematisches Forschungsinstitut Oberwolfach Report, vol. 55, p. 3160–3162, 2005.
      [Bibtex]
      @ARTICLE{Hamkins2005:TheGroundAxiom,
      AUTHOR = "Joel David Hamkins",
      TITLE = "The {Ground Axiom}",
      JOURNAL = "Mathematisches Forschungsinstitut Oberwolfach Report",
      YEAR = "2005",
      volume = "55",
      number = "",
      pages = "3160--3162",
      month = "",
      note = "",
      abstract = "",
      keywords = "",
      source = "",
      eprint = {1607.00723},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://jdh.hamkins.org/thegroundaxiom/},
      file = F,
      }
    • [DOI] J. D. Hamkins, “Infinitary computability with infinite time Turing machines,” in New Computational Paradigms, 2005.
      [Bibtex]
      @INPROCEEDINGS{Hamkins2005:InfinitaryComputabilityWithITTM,
      AUTHOR = "Joel David Hamkins",
      TITLE = "Infinitary computability with infinite time {Turing} machines",
      BOOKTITLE = "{New Computational Paradigms}",
      YEAR = "2005",
      editor = "B. Cooper and B. Löwe",
      volume = "3526",
      number = "",
      series = "LNCS",
      pages = "",
      address = "",
      month = "June 8-12",
      organization = "CiE",
      publisher = "Springer-Verlag",
      isbn = "3-540-26179-6",
      note = "",
      abstract = "",
      keywords = "",
      doi = {10.1007/11494645_22},
      ee = {},
      file = F,
      url = {http://wp.me/p5M0LV-2H},
      }
    • J. D. Hamkins, “book review of G.~Tourlakis, Lectures in Logic and Set Theory, vols.~I & II,” Bulletin of Symbolic Logic, vol. 11, iss. 2, p. 241, 2005.
      [Bibtex]
      @ARTICLE{Hamkins2005:TourlakisBookReview,
      AUTHOR = "Joel David Hamkins",
      TITLE = "book review of {G.~Tourlakis}, {Lectures in Logic and Set Theory}, vols.~{I \& II}",
      JOURNAL = "Bulletin of Symbolic Logic",
      YEAR = "2005",
      volume = "11",
      number = "2",
      pages = "241",
      month = "June",
      note = "",
      abstract = "",
      keywords = "book-review",
      source = "",
      url = "http://jdh.hamkins.org/tourlakisbookreview/",
      file = F,
      }
    • [DOI] J. D. Hamkins, “Supertask computation,” in Classical and New Paradigms of Computation and their Complexity Hierarchies, Dordrecht, 2004, p. 141–158, Papers of the conference “Foundations of the Formal Sciences III” held in Vienna, September 21-24, 2001.
      [Bibtex]
      @INPROCEEDINGS{Hamkins2004:SupertaskComputation,
      AUTHOR = {Hamkins, Joel David},
      TITLE = {Supertask computation},
      BOOKTITLE = {{Classical and New Paradigms of Computation and their Complexity Hierarchies}},
      SERIES = {Trends Log.~Stud.~Log.~Libr.},
      VOLUME = {23},
      PAGES = {141--158},
      PUBLISHER = {Kluwer Acad.~Publ.},
      ADDRESS = {Dordrecht},
      YEAR = {2004},
      MRCLASS = {03D10 (03D25 68Q05)},
      MRNUMBER = {2155535},
      DOI = {10.1007/978-1-4020-2776-5_8},
      URL = {http://jdh.hamkins.org/supertaskcomputation/},
      note = {Papers of the conference ``Foundations of the Formal Sciences III'' held in Vienna, September 21-24, 2001},
      eprint = {math/0212049},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      file = F,
      }
    • [DOI] J. D. Hamkins, “Extensions with the approximation and cover properties have no new large cardinals,” Fund.~Math., vol. 180, iss. 3, p. 257–277, 2003.
      [Bibtex]
      @article{Hamkins2003:ExtensionsWithApproximationAndCoverProperties,
      AUTHOR = {Hamkins, Joel David},
      TITLE = {Extensions with the approximation and cover properties have no new large cardinals},
      JOURNAL = {Fund.~Math.},
      FJOURNAL = {Fundamenta Mathematicae},
      VOLUME = {180},
      YEAR = {2003},
      NUMBER = {3},
      PAGES = {257--277},
      ISSN = {0016-2736},
      MRCLASS = {03E55 (03E40)},
      MRNUMBER = {2063629 (2005m:03100)},
      DOI = {10.4064/fm180-3-4},
      URL = {http://wp.me/p5M0LV-2B},
      eprint = {math/0307229},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      file = F,
      }
    • [DOI] J. D. Hamkins and P. D. Welch, “${\rm P}^f\neq {\rm NP}^f$ for almost all $f$,” Math.~Logic Q., vol. 49, iss. 5, p. 536–540, 2003.
      [Bibtex]
      @ARTICLE{HamkinsWelch2003:PfneqNPf,
      AUTHOR = {Hamkins, Joel David and Welch, Philip D.},
      TITLE = {{${\rm P}^f\neq {\rm NP}^f$} for almost all {$f$}},
      JOURNAL = {Math.~Logic Q.},
      FJOURNAL = {Mathematical Logic Quarterly},
      VOLUME = {49},
      YEAR = {2003},
      NUMBER = {5},
      PAGES = {536--540},
      ISSN = {0942-5616},
      MRCLASS = {03D65 (03D10 03E45 68Q05 68Q15)},
      MRNUMBER = {1998405 (2004m:03163)},
      MRREVIEWER = {Peter G.~Hinman},
      DOI = {10.1002/malq.200310057},
      URL = {http://jdh.hamkins.org/pf-npf/},
      eprint = {math/0212046},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      }
    • [DOI] A. W.~Apter and J. D. Hamkins, “Exactly controlling the non-supercompact strongly compact cardinals,” Journal of Symbolic Logic, vol. 68, iss. 2, p. 669–688, 2003.
      [Bibtex]
      @ARTICLE{ApterHamkins2003:ExactlyControlling,
      AUTHOR = {Arthur W.~Apter and Joel David Hamkins},
      TITLE = {Exactly controlling the non-supercompact strongly compact cardinals},
      JOURNAL = {Journal of Symbolic Logic},
      VOLUME = {68},
      YEAR = {2003},
      NUMBER = {2},
      PAGES = {669--688},
      ISSN = {0022-4812},
      CODEN = {JSYLA6},
      MRCLASS = {03E35 (03E55)},
      MRNUMBER = {1976597 (2004b:03075)},
      MRREVIEWER = {A.~Kanamori},
      doi = {10.2178/jsl/1052669070},
      eprint = {math/0301016},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://wp.me/p5M0LV-2x},
      }
    • [DOI] J. D. Hamkins, “A simple maximality principle,” Journal of Symbolic Logic, vol. 68, iss. 2, p. 527–550, 2003.
      [Bibtex]
      @article{Hamkins2003:MaximalityPrinciple,
      AUTHOR = {Hamkins, Joel David},
      TITLE = {A simple maximality principle},
      JOURNAL = {Journal of Symbolic Logic},
      VOLUME = {68},
      YEAR = {2003},
      NUMBER = {2},
      PAGES = {527--550},
      ISSN = {0022-4812},
      CODEN = {JSYLA6},
      MRCLASS = {03E35 (03E40)},
      MRNUMBER = {1976589 (2005a:03094)},
      MRREVIEWER = {Ralf-Dieter Schindler},
      DOI = {10.2178/jsl/1052669062},
      URL = {http://wp.me/p5M0LV-2v},
      month = {},
      eprint = {math/0009240},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      }
    • [DOI] J. D. Hamkins, “How tall is the automorphism tower of a group?,” in Logic and Algebra, Y. Zhang, Ed., Providence, RI: AMS, 2002, vol. 302, p. 49–57.
      [Bibtex]
      @INCOLLECTION{Hamkins2001:HowTall?,
      AUTHOR = {Hamkins, Joel David},
      TITLE = {How tall is the automorphism tower of a group?},
      BOOKTITLE = {{Logic and Algebra}},
      SERIES = {Contemporary Math.},
      VOLUME = {302},
      PAGES = {49--57},
      PUBLISHER = {AMS},
      ADDRESS = {Providence, RI},
      YEAR = {2002},
      MRCLASS = {20E36 (03E35 20A15 20F28)},
      MRNUMBER = {1928383 (2003g:20048)},
      MRREVIEWER = {Martyn R.~Dixon},
      editor = {Yi Zhang},
      doi = {10.1090/conm/302},
      url = {http://wp.me/s5M0LV-howtall},
      }
    • [DOI] A. W.~Apter and J. D. Hamkins, “Indestructibility and the level-by-level agreement between strong compactness and supercompactness,” Journal of Symbolic Logic, vol. 67, iss. 2, p. 820–840, 2002.
      [Bibtex]
      @ARTICLE{ApterHamkins2002:LevelByLevel,
      AUTHOR = {Arthur W.~Apter and Joel David Hamkins},
      TITLE = {Indestructibility and the level-by-level agreement between strong compactness and supercompactness},
      JOURNAL = {Journal of Symbolic Logic},
      VOLUME = {67},
      YEAR = {2002},
      NUMBER = {2},
      PAGES = {820--840},
      ISSN = {0022-4812},
      CODEN = {JSYLA6},
      MRCLASS = {03E35 (03E55)},
      MRNUMBER = {1905168 (2003e:03095)},
      MRREVIEWER = {Carlos A.~Di Prisco},
      DOI = {10.2178/jsl/1190150111},
      URL = {http://wp.me/p5M0LV-2i},
      eprint = {math/0102086},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      }
    • [DOI] J. D. Hamkins and A. Lewis, “Post’s problem for supertasks has both positive and negative solutions,” Arch.~Math.~Logic, vol. 41, iss. 6, p. 507–523, 2002.
      [Bibtex]
      @article{HamkinsLewis2002:PostProblem,
      AUTHOR = {Hamkins, Joel David and Lewis, Andrew},
      TITLE = {Post's problem for supertasks has both positive and negative solutions},
      JOURNAL = {Arch.~Math.~Logic},
      FJOURNAL = {Archive for Mathematical Logic},
      VOLUME = {41},
      YEAR = {2002},
      NUMBER = {6},
      PAGES = {507--523},
      ISSN = {0933-5846},
      CODEN = {AMLOEH},
      MRCLASS = {03D10 (68Q05)},
      MRNUMBER = {1923194 (2003f:03052)},
      MRREVIEWER = {Robert M.~Baer},
      DOI = {10.1007/s001530100112},
      URL = {http://jdh.hamkins.org/postproblem/},
      eprint = {math/9808128},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      }
    • J. D. Hamkins, “Infinite time Turing machines,” Minds and Machines, vol. 12, iss. 4, p. 521–539, 2002.
      [Bibtex]
      @ARTICLE{Hamkins2002:Turing,
      author = {Joel David Hamkins},
      title = {Infinite time {T}uring machines},
      journal = {Minds and Machines},
      year = {2002},
      volume = {12},
      number = {4},
      pages = {521--539},
      month = {},
      note = {Special issue devoted to hypercomputation},
      key = {},
      annote = {},
      eprint = {math/0212047},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://wp.me/p5M0LV-2e},
      }
    • [DOI] D. Fishkind, J. D. Hamkins, and B. Montero, “New inconsistencies in infinite utilitarianism,” Australasian Journal of Philosophy, vol. 80, iss. 2, p. 178–190, 2002.
      [Bibtex]
      @article{FishkindHamkinsMontero2002:NewInconsistencies,
      author = {Donniell Fishkind and Joel David Hamkins and Barbara Montero},
      title = {New inconsistencies in infinite utilitarianism},
      journal = {Australasian Journal of Philosophy},
      year = {2002},
      volume = {80},
      number = {2},
      pages = {178--190},
      month = {},
      note = {},
      key = {},
      annote = {},
      url = {http://jdh.hamkins.org/newinconsistencies},
      doi = {10.1093/ajp/80.2.178},
      }
    • [DOI] A. W.~Apter and J. D. Hamkins, “Indestructible weakly compact cardinals and the necessity of supercompactness for certain proof schemata,” Math.~Logic Q., vol. 47, iss. 4, p. 563–571, 2001.
      [Bibtex]
      @ARTICLE{ApterHamkins2001:IndestructibleWC,
      AUTHOR = {Arthur W.~Apter and Joel David Hamkins},
      TITLE = {Indestructible weakly compact cardinals and the necessity of supercompactness for certain proof schemata},
      JOURNAL = {Math.~Logic Q.},
      FJOURNAL = {Mathematical Logic Quarterly},
      VOLUME = {47},
      YEAR = {2001},
      NUMBER = {4},
      PAGES = {563--571},
      ISSN = {0942-5616},
      MRCLASS = {03E35 (03E55)},
      MRNUMBER = {1865776 (2003h:03078)},
      DOI = {10.1002/1521-3870(200111)47:4%3C563::AID-MALQ563%3E3.0.CO;2-%23},
      URL = {http://jdh.hamkins.org/indestructiblewc/},
      eprint = {math/9907046},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      }
    • [DOI] J. D. Hamkins, “Unfoldable cardinals and the GCH,” Journal of Symbolic Logic, vol. 66, iss. 3, p. 1186–1198, 2001.
      [Bibtex]
      @article{Hamkins2001:UnfoldableCardinals,
      AUTHOR = {Hamkins, Joel David},
      TITLE = {Unfoldable cardinals and the {GCH}},
      JOURNAL = {Journal of Symbolic Logic},
      VOLUME = {66},
      YEAR = {2001},
      NUMBER = {3},
      PAGES = {1186--1198},
      ISSN = {0022-4812},
      CODEN = {JSYLA6},
      MRCLASS = {03E55 (03E35 03E40)},
      MRNUMBER = {1856735 (2002i:03059)},
      MRREVIEWER = {Eva Coplakova},
      DOI = {10.2307/2695100},
      URL = {http://wp.me/p5M0LV-28},
      eprint = {math/9909029},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      }
    • [DOI] J. D. Hamkins, “Gap forcing,” Israel Journal of Mathematics, vol. 125, p. 237–252, 2001.
      [Bibtex]
      @article{Hamkins2001:GapForcing,
      AUTHOR = {Hamkins, Joel David},
      TITLE = {Gap forcing},
      JOURNAL = {Israel Journal of Mathematics},
      VOLUME = {125},
      YEAR = {2001},
      PAGES = {237--252},
      ISSN = {0021-2172},
      CODEN = {ISJMAP},
      MRCLASS = {03E40 (03E55)},
      MRNUMBER = {1853813 (2002h:03111)},
      MRREVIEWER = {Renling Jin},
      DOI = {10.1007/BF02773382},
      URL = {http://jdh.hamkins.org/gapforcing/},
      eprint = {math/9808011},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      }
    • J. D. Hamkins and D. E. Seabold, “Infinite Time Turing Machines With Only One Tape,” Math.~Logic Q., vol. 47, iss. 2, p. 271–287, 2001.
      [Bibtex]
      @article{HamkinsSeabold2001:OneTape,
      author = {Hamkins, Joel David and Seabold, Daniel Evan},
      title = {Infinite Time {Turing} Machines With Only One Tape},
      journal = {Math.~Logic Q.},
      volume = {47},
      number = {2},
      publisher = {WILEY-VCH Verlag Berlin GmbH},
      issn = {1521-3870},
      MRNUMBER = {1829946 (2002f:03074)},
      url = {http://jdh.hamkins.org/onetape/},
      doi = {10.1002/1521-3870(200105)47:2<271::AID-MALQ271>3.0.CO;2-6},
      pages = {271--287},
      keywords = {One-tape infinite Turing machine, Supertask computation},
      year = {2001},
      eprint = {math/9907044},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      }
    • [DOI] J. D. Hamkins, “The wholeness axioms and $V=\rm HOD$,” Arch.~Math.~Logic, vol. 40, iss. 1, p. 1–8, 2001.
      [Bibtex]
      @article{Hamkins2001:WholenessAxiom,
      AUTHOR = {Hamkins, Joel David},
      TITLE = {The wholeness axioms and {$V=\rm HOD$}},
      JOURNAL = {Arch.~Math.~Logic},
      FJOURNAL = {Archive for Mathematical Logic},
      VOLUME = {40},
      YEAR = {2001},
      NUMBER = {1},
      PAGES = {1--8},
      ISSN = {0933-5846},
      CODEN = {AMLOEH},
      MRCLASS = {03E35 (03E65)},
      MRNUMBER = {1816602 (2001m:03102)},
      MRREVIEWER = {Ralf-Dieter Schindler},
      DOI = {10.1007/s001530050169},
      URL = {http://wp.me/p5M0LV-1k},
      eprint = {math/9902079},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      }
    • [DOI] J. D. Hamkins and A. Lewis, “Infinite time Turing machines,” Journal of Symbolic Logic, vol. 65, iss. 2, p. 567–604, 2000.
      [Bibtex]
      @article {HamkinsLewis2000:InfiniteTimeTM,
      AUTHOR = {Hamkins, Joel David and Lewis, Andy},
      TITLE = {Infinite time {T}uring machines},
      JOURNAL = {Journal of Symbolic Logic},
      VOLUME = {65},
      YEAR = {2000},
      NUMBER = {2},
      PAGES = {567--604},
      ISSN = {0022-4812},
      CODEN = {JSYLA6},
      MRCLASS = {03D10 (03D25 68Q05)},
      MRNUMBER = {1771072 (2001g:03072)},
      MRREVIEWER = {Robert M.~Baer},
      DOI = {10.2307/2586556},
      URL = {http://jdh.hamkins.org/ittms/},
      eprint = {math/9808093},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      }
    • [DOI] J. D. Hamkins, “The lottery preparation,” Ann.~Pure Appl.~Logic, vol. 101, iss. 2-3, p. 103–146, 2000.
      [Bibtex]
      @article {Hamkins2000:LotteryPreparation,
      AUTHOR = {Hamkins, Joel David},
      TITLE = {The lottery preparation},
      JOURNAL = {Ann.~Pure Appl.~Logic},
      FJOURNAL = {Annals of Pure and Applied Logic},
      VOLUME = {101},
      YEAR = {2000},
      NUMBER = {2-3},
      PAGES = {103--146},
      ISSN = {0168-0072},
      CODEN = {APALD7},
      MRCLASS = {03E55 (03E40)},
      MRNUMBER = {1736060 (2001i:03108)},
      MRREVIEWER = {Klaas Pieter Hart},
      DOI = {10.1016/S0168-0072(99)00010-X},
      URL = {http://jdh.hamkins.org/lotterypreparation/},
      eprint = {math/9808012},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      }
    • [DOI] J. D. Hamkins and S. Thomas, “Changing the heights of automorphism towers,” Ann.~Pure Appl.~Logic, vol. 102, iss. 1-2, p. 139–157, 2000.
      [Bibtex]
      @article {HamkinsThomas2000:ChangingHeights,
      AUTHOR = {Hamkins, Joel David and Thomas, Simon},
      TITLE = {Changing the heights of automorphism towers},
      JOURNAL = {Ann.~Pure Appl.~Logic},
      FJOURNAL = {Annals of Pure and Applied Logic},
      VOLUME = {102},
      YEAR = {2000},
      NUMBER = {1-2},
      PAGES = {139--157},
      ISSN = {0168-0072},
      CODEN = {APALD7},
      MRCLASS = {20F28 (03E35 20A15)},
      MRNUMBER = {1732058 (2000m:20057)},
      MRREVIEWER = {Markus Junker},
      DOI = {10.1016/S0168-0072(99)00039-1},
      URL = {http://jdh.hamkins.org/changingheightsoverl/},
      eprint = {math/9703204},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      }
    • [DOI] J. D. Hamkins and W. Woodin, “Small forcing creates neither strong nor Woodin cardinals,” Proc.~Amer.~Math.~Soc., vol. 128, iss. 10, p. 3025–3029, 2000.
      [Bibtex]
      @article {HamkinsWoodin2000:SmallForcing,
      AUTHOR = {Hamkins, Joel David and Woodin, W.~Hugh},
      TITLE = {Small forcing creates neither strong nor {W}oodin cardinals},
      JOURNAL = {Proc.~Amer.~Math.~Soc.},
      FJOURNAL = {Proceedings of the American Mathematical Society},
      VOLUME = {128},
      YEAR = {2000},
      NUMBER = {10},
      PAGES = {3025--3029},
      ISSN = {0002-9939},
      CODEN = {PAMYAR},
      MRCLASS = {03E35 (03E55)},
      MRNUMBER = {1664390 (2000m:03121)},
      MRREVIEWER = {Carlos A.~Di Prisco},
      DOI = {10.1090/S0002-9939-00-05347-8},
      URL = {http://jdh.hamkins.org/smallforcing-w/},
      eprint = {math/9808124},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      }
    • [DOI] J. D. Hamkins and B. Montero, “With infinite utility, more needn’t be better,” Australasian Journal of Philosophy, vol. 78, iss. 2, p. 231–240, 2000.
      [Bibtex]
      @article{HamkinsMontero2000:MoreBetter,
      author = {Joel David Hamkins and Barbara Montero},
      title = {With infinite utility, more needn't be better},
      journal = {Australasian Journal of Philosophy},
      volume = {78},
      number = {2},
      year = {2000},
      pages = {231--240},
      url = {http://jdh.hamkins.org/infinite-utility-more-better},
      doi = {10.1080/00048400012349511},
      }
    • [DOI] J. D. Hamkins and B. Montero, “Utilitarianism in infinite worlds,” Utilitas, vol. 12, iss. 1, p. 91–96, 2000.
      [Bibtex]
      @article{HamkinsMontero2000:InfiniteWorlds,
      author = {Joel David Hamkins and Barbara Montero},
      title = {Utilitarianism in infinite worlds},
      journal = {Utilitas},
      volume = {12},
      number = {1},
      year = {2000},
      pages = {91--96},
      url = {http://jdh.hamkins.org/infiniteworlds},
      doi = {10.1017/S0953820800002648},
      }
    • [DOI] J. D. Hamkins, “book review of The Higher Infinite, Akihiro Kanamori,” Studia Logica, vol. 65, iss. 3, p. 443–446, 2000.
      [Bibtex]
      @ARTICLE{Hamkins2000:BookReviewKanamori,
      AUTHOR = "Joel David Hamkins",
      TITLE = "book review of {The Higher Infinite, Akihiro Kanamori}",
      JOURNAL = "Studia Logica",
      publisher = "Springer Netherlands",
      YEAR = "2000",
      volume = "65",
      number = "3",
      pages = "443--446",
      month = "",
      note = "",
      abstract = "",
      doi = "10.1023/A:1017327516639",
      url = "http://wp.me/p5M0LV-16",
      issn = "0039-3215",
      keywords = "book-review",
      source = "",
      file = F,
      }
    • [DOI] J. D. Hamkins, “Gap forcing: generalizing the Lévy-Solovay theorem,” Bulletin of Symbolic Logic, vol. 5, iss. 2, p. 264–272, 1999.
      [Bibtex]
      @article{Hamkins99:GapForcingGen,
      AUTHOR = {Hamkins, Joel David},
      TITLE = {Gap forcing: generalizing the {L}\'evy-{S}olovay theorem},
      JOURNAL = {Bulletin of Symbolic Logic},
      FJOURNAL = {The Bulletin of Symbolic Logic},
      VOLUME = {5},
      YEAR = {1999},
      NUMBER = {2},
      PAGES = {264--272},
      ISSN = {1079-8986},
      MRCLASS = {03E40 (03E55)},
      MRNUMBER = {1792281 (2002g:03106)},
      MRREVIEWER = {Carlos A.~Di Prisco},
      DOI = {10.2307/421092},
      URL = {http://jdh.hamkins.org/gapforcinggen/},
      month = {June},
      eprint = {math/9901108},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      }
    • A. W.~Apter and J. D. Hamkins, “Universal indestructibility,” Kobe Journal of Mathematics, vol. 16, iss. 2, p. 119–130, 1999.
      [Bibtex]
      @article {ApterHamkins99:UniversalIndestructibility,
      AUTHOR = {Arthur W.~Apter and Joel David Hamkins},
      TITLE = {Universal indestructibility},
      JOURNAL = {Kobe Journal of Mathematics},
      VOLUME = {16},
      YEAR = {1999},
      NUMBER = {2},
      PAGES = {119--130},
      ISSN = {0289-9051},
      MRCLASS = {03E55 (03E35)},
      MRNUMBER = {1745027 (2001k:03112)},
      MRNUMBER = {1 745 027},
      eprint = {math/9808004},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://wp.me/p5M0LV-12},
      }
    • J. D. Hamkins, “Using video and peer feedback to improve teaching,” Assessment Practices in Mathematics, MAA Notes, vol. 49, 1999.
      [Bibtex]
      @article{Hamkins99:VideoFeedback,
      author = {Joel David Hamkins},
      title = {Using video and peer feedback to improve teaching},
      journal = {Assessment Practices in Mathematics, MAA Notes},
      volume = {49},
      year = {1999},
      editor = {Bonnie Gold},
      }
    • [DOI] J. D. Hamkins and S. Shelah, “Superdestructibility: a dual to Laver’s indestructibility,” Journal of Symbolic Logic, vol. 63, iss. 2, p. 549–554, 1998.
      [Bibtex]
      @article {HamkinsShelah98:Dual,
      AUTHOR = {Hamkins, Joel David and Shelah, Saharon},
      TITLE = {Superdestructibility: a dual to {L}aver's indestructibility},
      JOURNAL = {Journal of Symbolic Logic},
      VOLUME = {63},
      YEAR = {1998},
      NUMBER = {2},
      PAGES = {549--554},
      ISSN = {0022-4812},
      CODEN = {JSYLA6},
      MRCLASS = {03E55 (03E40)},
      MRNUMBER = {1625927 (99m:03106)},
      MRREVIEWER = {Douglas R.~Burke},
      DOI = {10.2307/2586848},
      URL = {http://jdh.hamkins.org/dual/},
      note = {[HmSh:618]},
      eprint = {math/9612227},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      }
    • [DOI] J. D. Hamkins, “Small forcing makes any cardinal superdestructible,” Journal of Symbolic Logic, vol. 63, iss. 1, p. 51–58, 1998.
      [Bibtex]
      @article {Hamkins98:SmallForcing,
      AUTHOR = {Hamkins, Joel David},
      TITLE = {Small forcing makes any cardinal superdestructible},
      JOURNAL = {Journal of Symbolic Logic},
      VOLUME = {63},
      YEAR = {1998},
      NUMBER = {1},
      PAGES = {51--58},
      ISSN = {0022-4812},
      CODEN = {JSYLA6},
      MRCLASS = {03E40 (03E55)},
      MRNUMBER = {1607499 (99b:03068)},
      MRREVIEWER = {Jakub Jasi{\'n}ski},
      DOI = {10.2307/2586586},
      URL = {http://jdh.hamkins.org/superdestructibility/},
      eprint = {1607.00684},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      }
    • [DOI] J. D. Hamkins, “Destruction or preservation as you like it,” Annals of Pure and Applied Logic, vol. 91, iss. 2-3, p. 191–229, 1998.
      [Bibtex]
      @article {Hamkins98:AsYouLikeIt,
      AUTHOR = {Hamkins, Joel David},
      TITLE = {Destruction or preservation as you like it},
      JOURNAL = {Annals of Pure and Applied Logic},
      FJOURNAL = {Annals of Pure and Applied Logic},
      VOLUME = {91},
      YEAR = {1998},
      NUMBER = {2-3},
      PAGES = {191--229},
      ISSN = {0168-0072},
      CODEN = {APALD7},
      MRCLASS = {03E55 (03E35)},
      MRNUMBER = {1604770 (99f:03071)},
      MRREVIEWER = {Joan Bagaria},
      DOI = {10.1016/S0168-0072(97)00044-4},
      URL = {http://jdh.hamkins.org/asyoulikeit/},
      eprint = {1607.00683},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      }
    • [DOI] J. D. Hamkins, “Every group has a terminating transfinite automorphism tower,” Proc.~Amer.~Math.~Soc., vol. 126, iss. 11, p. 3223–3226, 1998.
      [Bibtex]
      @article {Hamkins98:EveryGroup,
      AUTHOR = {Hamkins, Joel David},
      TITLE = {Every group has a terminating transfinite automorphism tower},
      JOURNAL = {Proc.~Amer.~Math.~Soc.},
      FJOURNAL = {Proceedings of the American Mathematical Society},
      VOLUME = {126},
      YEAR = {1998},
      NUMBER = {11},
      PAGES = {3223--3226},
      ISSN = {0002-9939},
      CODEN = {PAMYAR},
      MRCLASS = {20E36 (20F28)},
      MRNUMBER = {1487370 (2000e:20057)},
      DOI = {10.1090/S0002-9939-98-04797-2},
      URL = {http://jdh.hamkins.org/everygroup/},
      eprint = {math/9808014},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      }
    • [DOI] J. D. Hamkins, “book review of Notes on Set Theory, Moschovakis,” Journal of Symbolic Logic, vol. 62, iss. 4, p. pp.~1493-1494, 1997.
      [Bibtex]
      @article{Hamkins1998:BookReviewMoschovakis,
      jstor_articletype = {book-review},
      title = {book review of {Notes on Set Theory, Moschovakis}},
      author = {Hamkins, Joel David},
      journal = {Journal of Symbolic Logic},
      jstor_issuetitle = {},
      volume = {62},
      number = {4},
      jstor_formatteddate = {Dec., 1997},
      pages = {pp.~1493-1494},
      ISSN = {00224812},
      keywords = {book-review},
      abstract = {},
      language = {English},
      year = {1997},
      publisher = {Association for Symbolic Logic},
      copyright = {Copyright © 1997 Association for Symbolic Logic},
      doi = {10.2307/2275660},
      url = {http://wp.me/p5M0LV-S},
      }
    • [DOI] J. D. Hamkins, “Canonical seeds and Prikry trees,” Journal of Symbolic Logic, vol. 62, iss. 2, p. 373–396, 1997.
      [Bibtex]
      @article {Hamkins97:Seeds,
      AUTHOR = {Hamkins, Joel David},
      TITLE = {Canonical seeds and {P}rikry trees},
      JOURNAL = {Journal of Symbolic Logic},
      FJOURNAL = {The Journal of Symbolic Logic},
      VOLUME = {62},
      YEAR = {1997},
      NUMBER = {2},
      PAGES = {373--396},
      ISSN = {0022-4812},
      CODEN = {JSYLA6},
      MRCLASS = {03E40 (03E05 03E55)},
      MRNUMBER = {1464105 (98i:03070)},
      MRREVIEWER = {Douglas R.~Burke},
      DOI = {10.2307/2275538},
      URL = {http://jdh.hamkins.org/seeds},
      }
    • [DOI] J. Hamkins, “Fragile measurability,” Journal of Symbolic Logic, vol. 59, iss. 1, p. 262–282, 1994.
      [Bibtex]
      @article {Hamkins94:FragileMeasurability,
      AUTHOR = {Hamkins, Joel},
      TITLE = {Fragile measurability},
      JOURNAL = {Journal of Symbolic Logic},
      VOLUME = {59},
      YEAR = {1994},
      NUMBER = {1},
      PAGES = {262--282},
      ISSN = {0022-4812},
      CODEN = {JSYLA6},
      MRCLASS = {03E35 (03E55)},
      MRNUMBER = {1264978 (95c:03129)},
      MRREVIEWER = {J.~M.~Henle},
      DOI = {10.2307/2275264},
      URL = {http://jdh.hamkins.org/fragilemeasurability/},
      }
    • J. D. Hamkins, “Lifting and extending measures; fragile measurability,” PhD Thesis, University of California, Berkeley, Department of Mathematics, 1994.
      [Bibtex]
      @PHDTHESIS{Hamkins94:Dissertation,
      author = {Joel David Hamkins},
      title = {Lifting and extending measures; fragile measurability},
      school = {University of California, Berkeley},
      institution = {University of California, Berkeley},
      year = {1994},
      address = {Department of Mathematics},
      month = {May},
      note = {},
      key = {},
      annote = {},
      url = {http://jdh.hamkins.org/dissertation/},
      }
    • J. D. Hamkins, Tutor On Paper, Berkeley, CA: Vargon Publishers, 1992, 93 pages.
      [Bibtex]
      @BOOK{TutorOnPaper,
      author = {Joel David Hamkins},
      title = {{Tutor On Paper}},
      publisher = {Vargon Publishers},
      year = {1992},
      address = {Berkeley, CA},
      note = {93 pages},
      keywords = {book},
      }
    • D. Fishkind, J. D. Hamkins, and B. Montero, “A Reply to Lauwers,” , 2002.
      [Bibtex]
      @article{ReplyToLauwers,
      author = {Donniell Fishkind and Joel David Hamkins and Barbara Montero},
      title = {A Reply to {Lauwers}},
      year= {2002},
      journal = {},
      note = {2 pages},
      keywords = {noCV},
      }
    • J. D. Hamkins, “A class of strong diamond principles,” ArXiv e-prints, 2002.
      [Bibtex]
      @ARTICLE{Hamkins:LaverDiamond,
      author = {Joel David Hamkins},
      title = {A class of strong diamond principles},
      journal = {ArXiv e-prints},
      year = {2002},
      eprint = {math/0211419},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://wp.me/p5M0LV-C},
      }
    • J. D. Hamkins, Forcing and Large Cardinals, , 2005, Book manuscript, in preparation, 225 pages.
      [Bibtex]
      @BOOK{Hamkins:ForcingAndLargeCardinals,
      AUTHOR = "Joel David Hamkins",
      editor = "",
      TITLE = "{Forcing and Large Cardinals}",
      PUBLISHER = "",
      YEAR = "2005",
      volume = "",
      number = "",
      series = "",
      address = "",
      edition = "",
      month = "",
      note = "Book manuscript, in preparation, 225 pages",
      abstract = "",
      isbn = "",
      price = "",
      keywords = "book,inprep,noCV",
      source = "",
      file = F,
      }
  • Fregean abstraction in Zermelo-Fraenkel set theory: a deflationary account
    • [DOI] J. D. Hamkins, “Fregean abstraction in Zermelo-Fraenkel set theory: a deflationary account,” Mathematics arXiv, 2022.
      [Bibtex]
      @article{Hamkins:Fregean-abstraction-deflationary-account,
      author = {Hamkins, Joel David},
      title = {Fregean abstraction in Zermelo-Fraenkel set theory: a deflationary account},
      doi = {10.48550/ARXIV.2209.07845},
      eprint = {2209.07845},
      archivePrefix={arXiv},
      primaryClass={math.LO},
      journal = {Mathematics arXiv},
      year = {2022},
      url = {http://jdh.hamkins.org/fregean-abstraction-deflationary-account},
      }
  • Nonlinearity and illfoundedness in the hierarchy of large cardinal consistency strength

    J. D. Hamkins, Nonlinearity and illfoundedness in the hierarchy of large cardinal consistency strength arXiv, 2022. [Bibtex] @misc{Hamkins:Nonlinearity-in-the-hierarchy-of-large-cardinal-consistency-strength, author = {Joel David Hamkins}, title = {Nonlinearity and illfoundedness in the hierarchy of large cardinal consistency strength}, publisher = {arXiv}, year …

  • Reflection in second-order set theory with abundant urelements bi-interprets a supercompact cardinal

    J. D. Hamkins and B. Yao, “Reflection in second-order set theory with abundant urelements bi-interprets a supercompact cardinal,” Mathematics arXiv, 2022. [Bibtex] @ARTICLE{HamkinsYao:Reflection-in-second-order-set-theory-with-abundant-urelements, author={Joel David Hamkins and Bokai Yao}, year={2022}, eprint={2204.09766}, archivePrefix={arXiv}, primaryClass={math.LO}, title = {Reflection in second-order set theory …

  • Infinite Wordle and the Mastermind numbers
    • J. D. Hamkins, “Infinite Wordle and the mastermind numbers,” Mathematics arXiv, 2022.
      [Bibtex]
      @ARTICLE{Hamkins:Infinite-Wordle-and-the-mastermind-numbers,
      author = {Joel David Hamkins},
      title = {Infinite Wordle and the mastermind numbers},
      journal = {Mathematics arXiv},
      year = {2022},
      volume = {},
      number = {},
      pages = {},
      month = {},
      note = {Under review},
      abstract = {},
      keywords = {under-review},
      source = {},
      doi = {},
      eprint = {2203.06804},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://jdh.hamkins.org/infinite-wordle-mastermind},
      }
  • Infinite Hex is a draw
    • J. D. Hamkins and D. Leonessi, “Infinite Hex is a draw,” Mathematics arXiv, 2022.
      [Bibtex]
      @ARTICLE{HamkinsLeonessi:Infinite-Hex-is-a-draw,
      author = {Joel David Hamkins and Davide Leonessi},
      title = {Infinite Hex is a draw},
      journal = {Mathematics arXiv},
      year = {2022},
      volume = {},
      number = {},
      pages = {},
      month = {},
      note = {Under review},
      abstract = {},
      keywords = {under-review},
      source = {},
      doi = {},
      eprint = {2201.06475},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://jdh.hamkins.org/infinite-hex-is-a-draw},
      }
  • Transfinite game values in infinite draughts
    • J. D. Hamkins and D. Leonessi, “Transfinite game values in infinite draughts,” Mathematics arXiv, 2021.
      [Bibtex]
      @ARTICLE{HamkinsLeonessi:Transfinite-game-values-in-infinite-draughts,
      author = {Joel David Hamkins and Davide Leonessi},
      title = {Transfinite game values in infinite draughts},
      journal = {Mathematics arXiv},
      year = {2021},
      volume = {},
      number = {},
      pages = {},
      month = {},
      note = {Under review},
      abstract = {},
      keywords = {under-review},
      source = {},
      doi = {},
      eprint = {2111.02053},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://jdh.hamkins.org/transfinite-game-values-in-infinite-draughts},
      }
  • Is the twin prime conjecture independent of Peano Arithmetic?
    • A. Berarducci, A. Fornasiero, and J. D. Hamkins, “Is the twin prime conjecture independent of Peano Arithmetic?,” Mathematics arXiv, 2021.
      [Bibtex]
      @ARTICLE{BerarducciFornasieroHamkins:Is-the-twin-prime-conjecture-independent-of-PA,
      author = {Alessandro Berarducci and Antongiulio Fornasiero and Joel David Hamkins},
      title = {Is the twin prime conjecture independent of Peano Arithmetic?},
      journal = {Mathematics arXiv},
      year = {2021},
      volume = {},
      number = {},
      pages = {},
      month = {},
      note = {Under review},
      abstract = {},
      keywords = {under-review},
      source = {},
      doi = {},
      eprint = {2110.08640},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://jdh.hamkins.org/is-the-twin-prime-conjecture-independent-of-peano-arithmetic/},
      }
  • Book review, Catarina Dutilh Novaes, The dialogical roots of deduction

    In this insightful and remarkable work, Professor Novaes defends and explores at length the philosophical thesis that mathematical proof and deduction generally has a fundamentally dialogical nature, proceeding in a back-and-forth dialogue between two semi-adversarial but collaborative actors, the Prover …

  • Nonlinearity in the hierarchy of large cardinal consistency strength

    This is currently a draft version only of my article-in-progress on the topic of linearity in the hierarchy of consistency strength, especially with large cardinals. Comments are very welcome, since I am still writing the article. Please kindly send me …

  • Proof and the Art of Mathematics: Examples and Extensions

    A companion volume to my proof-writing book, Proof and the Art of Mathematics. J. D. Hamkins, Proof and the Art of Mathematics: Examples and Extensions, MIT Press, 2021. [Bibtex] @BOOK{Hamkins2021:Proof-and-the-art-examples, author = {Joel David Hamkins}, title = {{Proof and the …

  • Lectures on the Philosophy of Mathematics
    • J. D. Hamkins, Lectures on the Philosophy of Mathematics, MIT Press, 2021.
      [Bibtex]
      @BOOK{Hamkins2021:Lectures-on-the-philosophy-of-mathematics,
      author = {Joel David Hamkins},
      editor = {},
      title = {{Lectures on the Philosophy of Mathematics}},
      publisher = {MIT Press},
      year = {2021},
      volume = {},
      number = {},
      series = {},
      address = {},
      edition = {},
      month = {},
      note = {},
      abstract = {},
      isbn = {9780262542234},
      price = {},
      keywords = {book},
      source = {},
      url = {https://mitpress.mit.edu/books/lectures-philosophy-mathematics},
      }
  • Modal model theory
    • J. D. Hamkins and W. A. Wołoszyn, “Modal model theory,” Mathematics ArXiv, 2020.
      [Bibtex]
      @ARTICLE{HamkinsWoloszyn:Modal-model-theory,
      title={Modal model theory},
      author={Joel David Hamkins and Wojciech Aleksander Wołoszyn},
      journal = {Mathematics ArXiv},
      year={2020},
      eprint={2009.09394},
      archivePrefix={arXiv},
      primaryClass={math.LO},
      note = {Under review},
      abstract = {},
      keywords = {under-review},
      source = {},
      doi = {},
      }
  • Categorical large cardinals and the tension between categoricity and set-theoretic reflection
    • J. D. Hamkins and R. Solberg, “Categorical large cardinals and the tension between categoricity and set-theoretic reflection,” Mathematics ArXiv, 2020.
      [Bibtex]
      @ARTICLE{HamkinsSolberg:Categorical-large-cardinals,
      author = {Joel David Hamkins and Robin Solberg},
      title = {Categorical large cardinals and the tension between categoricity and set-theoretic reflection},
      journal = {Mathematics ArXiv},
      year = {2020},
      volume = {},
      number = {},
      pages = {},
      month = {},
      note = {Under review},
      abstract = {},
      keywords = {under-review},
      url = {http://jdh.hamkins.org/categorical-large-cardinals/},
      source = {},
      doi = {},
      eprint = {2009.07164},
      archivePrefix ={arXiv},
      primaryClass = {math.LO}
      }
  • Choiceless large cardinals and set-theoretic potentialism
    • R. Cutolo and J. D. Hamkins, “Choiceless large cardinals and set-theoretic potentialism,” Mathematical Logic Quarterly, p. 10 pages, 2022.
      [Bibtex]
      @ARTICLE{CutoloHamkins:Choiceless-large-cardinals-and-set-theoretic-potentialism,
      author = {Raffaella Cutolo and Joel David Hamkins},
      title = {Choiceless large cardinals and set-theoretic potentialism},
      journal = {Mathematical Logic Quarterly},
      year = {2022},
      volume = {},
      number = {},
      pages = {10 pages},
      month = {},
      note = {to appear},
      abstract = {},
      keywords = {},
      source = {},
      doi = {},
      url = {http://jdh.hamkins.org/choiceless-large-cardinals-and-set-theoretic-potentialism},
      eprint = {2007.01690},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      }
  • Forcing as a computational process
    • J. D. Hamkins, R. Miller, and K. J. Williams, “Forcing as a computational process,” Mathematics ArXiv, 2020.
      [Bibtex]
      @ARTICLE{HamkinsMillerWilliams:Forcing-as-a-computational-process,
      author = {Joel David Hamkins and Russell Miller and Kameryn J. Williams},
      title = {Forcing as a computational process},
      journal = {Mathematics ArXiv},
      year = {2020},
      volume = {},
      number = {},
      pages = {},
      month = {},
      note = {Under review},
      abstract = {},
      keywords = {under-review},
      source = {},
      doi = {},
      url = {http://jdh.hamkins.org/forcing-as-a-computational-process},
      eprint = {2007.00418},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      }
  • My view of Univ
    • J. D. Hamkins, My view of Univ , The Martlet, Issue 11, Spring 2020, University College, Oxford, 2020.
      [Bibtex]
      @MISC{Hamkins2020:My-view-of-univ,
      author = {Joel David Hamkins},
      title = {My view of Univ},
      howpublished = {},
      year = {2020},
      month = {},
      note = {The Martlet, Issue 11, Spring 2020, University College, Oxford},
      abstract = {},
      keywords = {noCV},
      source = {},
      url = {https://t.co/3tqVwfD4uZ},
      }
  • Proof and the Art of Mathematics
    • J. D. Hamkins, Proof and the Art of Mathematics, MIT Press, 2020.
      [Bibtex]
      @BOOK{Hamkins2020:Proof-and-the-art-of-mathematics,
      author = {Joel David Hamkins},
      title = {Proof and the {Art} of {Mathematics}},
      publisher = {MIT Press},
      year = {2020},
      isbn = {978-0-262-53979-1},
      keywords = {book},
      url = {https://mitpress.mit.edu/books/proof-and-art-mathematics},
      }
  • Bi-interpretation in weak set theories
  • The $\Sigma_1$-definable universal finite sequence
    • [DOI] J. D. Hamkins and K. J. Williams, “The $\Sigma_1$-definable universal finite sequence,” Journal of Symbolic Logic, 2021.
      [Bibtex]
      @ARTICLE{HamkinsWilliams2021:The-universal-finite-sequence,
      author = {Joel David Hamkins and Kameryn J. Williams},
      title = {The $\Sigma_1$-definable universal finite sequence},
      journal = {Journal of Symbolic Logic},
      year = {2021},
      volume = {},
      number = {},
      pages = {},
      month = {},
      note = {},
      abstract = {},
      keywords = {},
      eprint = {1909.09100},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      source = {},
      doi = {10.1017/jsl.2020.59},
      }
  • Representing Ordinal Numbers with Arithmetically Interesting Sets of Real Numbers
    • D. D. Blair, J. D. Hamkins, and K. O’Bryant, “Representing Ordinal Numbers with Arithmetically Interesting Sets of Real Numbers,” Integers, vol. 20A, 2020.
      [Bibtex]
      @ARTICLE{BlairHamkinsOBryant2020:Representing-ordinal-numbers-with-arithmetically-interesting-sets-of-real-numbers,
      author = {D. Dakota Blair and Joel David Hamkins and Kevin O'Bryant},
      title = {Representing Ordinal Numbers with Arithmetically Interesting Sets of Real Numbers},
      journal = {Integers},
      FJOURNAL = {Integers Electronic Journal of Combinatorial Number Theory},
      year = {2020},
      volume = {20A},
      number = {},
      pages = {},
      month = {},
      note = {Paper~A3, \url{http://math.colgate.edu/~integers/vol20a.html}},
      abstract = {},
      keywords = {},
      source = {},
      doi = {},
      url = {https://wp.me/p5M0LV-1Tg},
      eprint = {1905.13123},
      archivePrefix = {arXiv},
      primaryClass = {math.NT},
      }
  • Kelley-Morse set theory does not prove the class Fodor principle
    • [DOI] V. Gitman, J. D. Hamkins, and A. Karagila, “Kelley-Morse set theory does not prove the class Fodor theorem,” Fundamenta Mathematicae, vol. 254, iss. 2, p. 133–154, 2021.
      [Bibtex]
      @ARTICLE{GitmanHamkinsKaragila:KM-set-theory-does-not-prove-the-class-Fodor-theorem,
      author = {Victoria Gitman and Joel David Hamkins and Asaf Karagila},
      title = {Kelley-Morse set theory does not prove the class {F}odor theorem},
      journal = {Fundamenta Mathematicae},
      VOLUME = {254},
      YEAR = {2021},
      NUMBER = {2},
      PAGES = {133--154},
      ISSN = {0016-2736},
      MRCLASS = {03E70 (03E25 03E35)},
      MRNUMBER = {4241500},
      DOI = {10.4064/fm725-9-2020},
      keywords = {},
      eprint = {1904.04190},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      source = {},
      url = {http://wp.me/p5M0LV-1RD},
      }
  • The axiom of well-ordered replacement is equivalent to full replacement over Zermelo + foundation

    In recent work, Alfredo Roque Freire and I have realized that the axiom of well-ordered replacement is equivalent to the full replacement axiom, over the Zermelo set theory with foundation. The well-ordered replacement axiom is the scheme asserting that if …

  • Set-theoretic blockchains
    • [DOI] M. E. Habič, J. D. Hamkins, L. D. Klausner, J. Verner, and K. J. Williams, “Set-theoretic blockchains,” Archive for Mathematical Logic, 2019.
      [Bibtex]
      @ARTICLE{HabicHamkinsKlausnerVernerWilliams2018:Set-theoretic-blockchains,
      author = {Miha E. Habič and Joel David Hamkins and Lukas Daniel Klausner and Jonathan Verner and Kameryn J. Williams},
      title = {Set-theoretic blockchains},
      journal="Archive for Mathematical Logic",
      year="2019",
      month="Mar",
      day="26",
      abstract="Given a countable model of set theory, we study the structure of its generic multiverse, the collection of its forcing extensions and ground models, ordered by inclusion. Mostowski showed that any finite poset embeds into the generic multiverse while preserving the nonexistence of upper bounds. We obtain several improvements of his result, using what we call the blockchain construction to build generic objects with varying degrees of mutual genericity. The method accommodates certain infinite posets, and we can realize these embeddings via a wide variety of forcing notions, while providing control over lower bounds as well. We also give a generalization to class forcing in the context of second-order set theory, and exhibit some further structure in the generic multiverse, such as the existence of exact pairs.",
      issn="1432-0665",
      doi="10.1007/s00153-019-00672-z",
      note = {},
      abstract = {},
      eprint = {1808.01509},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      keywords = {},
      source = {},
      url = {http://wp.me/p5M0LV-1M8},
      }
  • Topological models of arithmetic
  • Open class determinacy is preserved by forcing
    • J. D. Hamkins and H. W. Woodin, “Open class determinacy is preserved by forcing,” Mathematics ArXiv, p. 1–14, 2018.
      [Bibtex]
      @ARTICLE{HamkinsWoodin2018:Open-class-determinacy-is-preserved-by-forcing,
      author = {Joel David Hamkins and W. Hugh Woodin},
      title = {Open class determinacy is preserved by forcing},
      journal = {Mathematics ArXiv},
      year = {2018},
      volume = {},
      number = {},
      pages = {1--14},
      month = {},
      note = {Under review},
      abstract = {},
      eprint = {1806.11180},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      keywords = {under-review},
      source = {},
      doi = {},
      url = {http://wp.me/p5M0LV-1KF},
      }
  • The subseries number
    • [DOI] J. Brendle, W. Brian, and J. D. Hamkins, “The subseries number,” Fund. Math., vol. 247, iss. 1, p. 49–85, 2019.
      [Bibtex]
      @ARTICLE{BrendleBrianHamkins2019:The-subseries-number,
      AUTHOR = {Brendle, J\"{o}rg and Brian, Will and Hamkins, Joel David},
      TITLE = {The subseries number},
      JOURNAL = {Fund. Math.},
      FJOURNAL = {Fundamenta Mathematicae},
      VOLUME = {247},
      YEAR = {2019},
      NUMBER = {1},
      PAGES = {49--85},
      ISSN = {0016-2736},
      MRCLASS = {03E17 (03E35 40A05)},
      MRNUMBER = {3984279},
      DOI = {10.4064/fm667-11-2018},
      url = {http://jdh.hamkins.org/the-subseries-number},
      eprint = {1801.06206},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      }
  • The modal logic of arithmetic potentialism and the universal algorithm
    • J. D. Hamkins, “The modal logic of arithmetic potentialism and the universal algorithm,” Mathematics ArXiv, p. 1–35, 2018.
      [Bibtex]
      @ARTICLE{Hamkins:The-modal-logic-of-arithmetic-potentialism,
      author = {Joel David Hamkins},
      title = {The modal logic of arithmetic potentialism and the universal algorithm},
      journal = {Mathematics ArXiv},
      year = {2018},
      volume = {},
      number = {},
      pages = {1--35},
      month = {},
      eprint = {1801.04599},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      note = {Under review},
      url = {http://wp.me/p5M0LV-1Dh},
      abstract = {},
      keywords = {under-review},
      source = {},
      doi = {},
      }
  • The universal finite set
    • J. D. Hamkins and H. W. Woodin, “The universal finite set,” Mathematics ArXiv, p. 1–16, 2017.
      [Bibtex]
      @ARTICLE{HamkinsWoodin:The-universal-finite-set,
      author = {Joel David Hamkins and W. Hugh Woodin},
      title = {The universal finite set},
      journal = {Mathematics ArXiv},
      year = {2017},
      volume = {},
      number = {},
      pages = {1--16},
      month = {},
      note = {Manuscript under review},
      abstract = {},
      keywords = {under-review},
      source = {},
      doi = {},
      eprint = {1711.07952},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://jdh.hamkins.org/the-universal-finite-set},
      }
  • The set-theoretic universe is not necessarily a class-forcing extension of HOD
    • J. D. Hamkins and J. Reitz, “The set-theoretic universe $V$ is not necessarily a class-forcing extension of HOD,” Mathematics ArXiv, 2017.
      [Bibtex]
      @ARTICLE{HamkinsReitz:The-set-theoretic-universe-is-not-necessarily-a-forcing-extension-of-HOD,
      author = {Joel David Hamkins and Jonas Reitz},
      title = {The set-theoretic universe {$V$} is not necessarily a class-forcing extension of {HOD}},
      journal = {Mathematics ArXiv},
      year = {2017},
      volume = {},
      number = {},
      pages = {},
      month = {September},
      note = {Manuscript under review},
      abstract = {},
      keywords = {under-review},
      source = {},
      doi = {},
      eprint = {1709.06062},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://jdh.hamkins.org/the-universe-need-not-be-a-class-forcing-extension-of-hod},
      }
  • Inner-model reflection principles
    • [DOI] N. Barton, A. E. Caicedo, G. Fuchs, J. D. Hamkins, J. Reitz, and R. Schindler, “Inner-model reflection principles,” Studia Logica, vol. 108, p. 573–595, 2020.
      [Bibtex]
      @ARTICLE{BartonCaicedoFuchsHamkinsReitzSchindler2020:Inner-model-reflection-principles,
      author = {Neil Barton and Andr\'es Eduardo Caicedo and Gunter Fuchs and Joel David Hamkins and Jonas Reitz and Ralf Schindler},
      title = {Inner-model reflection principles},
      journal = {Studia Logica},
      year = {2020},
      volume = {108},
      number = {},
      pages = {573--595},
      month = {},
      note = {},
      abstract = {},
      keywords = {},
      source = {},
      doi = {10.1007/s11225-019-09860-7},
      eprint = {1708.06669},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://jdh.hamkins.org/inner-model-reflection-principles},
      }
  • The modal logic of set-theoretic potentialism and the potentialist maximality principles
  • Boolean ultrapowers, the Bukovský-Dehornoy phenomenon, and iterated ultrapowers
    • G. Fuchs and J. D. Hamkins, “The Bukovský-Dehornoy phenomenon for Boolean ultrapowers,” ArXiv e-prints, 2017.
      [Bibtex]
      @ARTICLE{FuchsHamkins:TheBukovskyDehornoyPhenomenonForBooleanUltrapowers,
      AUTHOR = {Gunter Fuchs and Joel David Hamkins},
      TITLE = {The {Bukovsk\'y-Dehornoy} phenomenon for {Boolean} ultrapowers},
      JOURNAL = {ArXiv e-prints},
      YEAR = {2017},
      volume = {},
      number = {},
      pages = {},
      month = {},
      note = {Under review},
      abstract = {},
      keywords = {under-review},
      source = {},
      eprint = {1707.06702},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://wp.me/p5M0LV-1zz},
      }
  • The exact strength of the class forcing theorem

    Abstract. The class forcing theorem, which asserts that every class forcing notion $\newcommand\P{\mathbb{P}}\P$ admits a forcing relation $\newcommand\forces{\Vdash}\forces_\P$, that is, a relation satisfying the forcing relation recursion — it follows that statements true in the corresponding forcing extensions are forced …

  • When does every definable nonempty set have a definable element?
    • F. G. Dorais and J. D. Hamkins, “When does every definable nonempty set have a definable element?,” Mathematical Logic Quarterly, vol. 65, iss. 4, pp. 407-411, 2019.
      [Bibtex]
      @ARTICLE{DoraisHamkins:When-does-every-definable-nonempty-set-have-a-definable-element,
      author = {Dorais, François G. and Hamkins, Joel David},
      title = {When does every definable nonempty set have a definable element?},
      journal = {Mathematical Logic Quarterly},
      volume = {65},
      number = {4},
      pages = {407-411},
      doi = {10.1002/malq.201700035},
      abstract = {Abstract The assertion that every definable set has a definable element is equivalent over ZF to the principle V=HOD, and indeed, we prove, so is the assertion merely that every Π2-definable set has an ordinal-definable element. Meanwhile, every model of ZFC has a forcing extension satisfying V≠HOD in which every Σ2-definable set has an ordinal-definable element. Similar results hold for HOD(R) and HOD(Ordω) and other natural instances of HOD(X).},
      year = {2019},
      keywords = {},
      source = {},
      doi = {},
      eprint = {1706.07285},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://jdh.hamkins.org/definable-sets-with-definable-elements},
      }
  • A model of the generic Vopěnka principle in which the ordinals are not $\Delta_2$-Mahlo
    • [DOI] V. Gitman and J. D. Hamkins, “A model of the generic Vopěnka principle in which the ordinals are not Mahlo,” Archive for Mathematical Logic, p. 1–21, 2018.
      [Bibtex]
      @ARTICLE{GitmanHamkins2018:A-model-of-the-generic-Vopenka-principle-in-which-the-ordinals-are-not-Mahlo,
      author = {Gitman, Victoria and Hamkins, Joel David},
      year = {2018},
      title = {A model of the generic Vopěnka principle in which the ordinals are not Mahlo},
      journal = {Archive for Mathematical Logic},
      issn = {0933-5846},
      doi = {10.1007/s00153-018-0632-5},
      month = {5},
      pages = {1--21},
      eprint = {1706.00843},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://wp.me/p5M0LV-1xT},
      abstract = {The generic Vopěnka principle, we prove, is relatively consistent with the ordinals being non-Mahlo. Similarly, the generic Vopěnka scheme is relatively consistent with the ordinals being definably non-Mahlo. Indeed, the generic Vopěnka scheme is relatively consistent with the existence of a Δ2-definable class containing no regular cardinals. In such a model, there can be no Σ2-reflecting cardinals and hence also no remarkable cardinals. This latter fact answers negatively a question of Bagaria, Gitman and Schindler.},
      }
  • The inclusion relations of the countable models of set theory are all isomorphic
    • J. D. Hamkins and M. Kikuchi, “The inclusion relations of the countable models of set theory are all isomorphic,” ArXiv e-prints, 2017.
      [Bibtex]
      @ARTICLE{HamkinsKikuchi:The-inclusion-relations-of-the-countable-models-of-set-theory-are-all-isomorphic,
      author = {Joel David Hamkins and Makoto Kikuchi},
      title = {The inclusion relations of the countable models of set theory are all isomorphic},
      journal = {ArXiv e-prints},
      editor = {},
      year = {2017},
      volume = {},
      number = {},
      pages = {},
      month = {},
      doi = {},
      note = {Manuscript under review},
      eprint = {1704.04480},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://jdh.hamkins.org/inclusion-relations-are-all-isomorphic},
      abstract = {},
      keywords = {under-review},
      source = {},
      }
  • Computable quotient presentations of models of arithmetic and set theory
    • [DOI] M. T. Godziszewski and J. D. Hamkins, “Computable Quotient Presentations of Models of Arithmetic and Set Theory,” in Logic, Language, Information, and Computation: 24th International Workshop, WoLLIC 2017, London, UK, July 18-21, 2017, Proceedings, J. Kennedy and R. J. G. B. de Queiroz, Eds., Springer, 2017, p. 140–152.
      [Bibtex]
      @Inbook{GodziszewskiHamkins2017:Computable-quotient-presentations-of-models-of-arithmetic-and-set-theory,
      author="Godziszewski, Micha{\l} Tomasz and Hamkins, Joel David",
      editor="Kennedy, Juliette and de Queiroz, Ruy J.G.B.",
      title="Computable Quotient Presentations of Models of Arithmetic and Set Theory",
      bookTitle="{Logic, Language, Information, and Computation: 24th International Workshop, WoLLIC 2017, London, UK, July 18-21, 2017, Proceedings}",
      year="2017",
      publisher="Springer",
      address="",
      pages="140--152",
      abstract="We prove various extensions of the Tennenbaum phenomenon to the case of computable quotient presentations of models of arithmetic and set theory. Specifically, no nonstandard model of arithmetic has a computable quotient presentation by a c.e. equivalence relation. No {\$}{\$}{\backslash}Sigma {\_}1{\$}{\$} -sound nonstandard model of arithmetic has a computable quotient presentation by a co-c.e. equivalence relation. No nonstandard model of arithmetic in the language {\$}{\$}{\backslash}{\{}+,{\backslash}cdot ,{\backslash}le {\backslash}{\}}{\$}{\$} has a computably enumerable quotient presentation by any equivalence relation of any complexity. No model of ZFC or even much weaker set theories has a computable quotient presentation by any equivalence relation of any complexity. And similarly no nonstandard model of finite set theory has a computable quotient presentation.",
      isbn="978-3-662-55386-2",
      doi="10.1007/978-3-662-55386-2_10",
      eprint = {1702.08350},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://wp.me/p5M0LV-1tW},
      }
  • The implicitly constructible universe
    • [DOI] M. J. Groszek and J. D. Hamkins, “The implicitly constructible universe,” Journal of Symbolic Logic, vol. 84, iss. 4, p. 1403–1421, 2019.
      [Bibtex]
      @ARTICLE{GroszekHamkins2019:The-implicitly-constructible-universe,
      AUTHOR = {Groszek, Marcia J. and Hamkins, Joel David},
      TITLE = {The implicitly constructible universe},
      JOURNAL = {Journal of Symbolic Logic},
      FJOURNAL = {The Journal of Symbolic Logic},
      VOLUME = {84},
      YEAR = {2019},
      NUMBER = {4},
      PAGES = {1403--1421},
      ISSN = {0022-4812},
      MRCLASS = {03E35 (03E45)},
      MRNUMBER = {4045982},
      DOI = {10.1017/jsl.2018.57},
      eprint = {1702.07947},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://jdh.hamkins.org/the-implicitly-constructible-universe},
      }
  • The rearrangement number
    • [DOI] A. Blass, J. Brendle, W. Brian, J. D. Hamkins, M. Hardy, and P. B. Larson, “The rearrangement number,” Trans. Amer. Math. Soc., vol. 373, iss. 1, p. 41–69, 2020.
      [Bibtex]
      @ARTICLE{BlassBrendleBrianHamkinsHardyLarson2020:TheRearrangementNumber,
      author = {Andreas Blass and Jörg Brendle and Will Brian and Joel David Hamkins and Michael Hardy and Paul B. Larson},
      title = {The rearrangement number},
      JOURNAL = {Trans. Amer. Math. Soc.},
      FJOURNAL = {Transactions of the American Mathematical Society},
      VOLUME = {373},
      YEAR = {2020},
      NUMBER = {1},
      PAGES = {41--69},
      ISSN = {0002-9947},
      MRCLASS = {03E17 (03E35 40A05)},
      MRNUMBER = {4042868},
      DOI = {10.1090/tran/7881},
      note = {},
      url = {http://jdh.hamkins.org/the-rearrangement-number},
      eprint = {1612.07830},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      abstract = {},
      keywords = {},
      source = {},
      }
  • Ord is not definably weakly compact
    • [DOI] A. Enayat and J. D. Hamkins, “ZFC proves that the class of ordinals is not weakly compact for definable classes,” Journal of Symbolic Logic, vol. 83, iss. 1, p. 146–164, 2018.
      [Bibtex]
      @ARTICLE{EnayatHamkins2018:Ord-is-not-definably-weakly-compact,
      author = {Ali Enayat and Joel David Hamkins},
      title = {{ZFC} proves that the class of ordinals is not weakly compact for definable classes},
      journal = {Journal of Symbolic Logic},
      year = {2018},
      volume = {83},
      number = {1},
      pages = {146--164},
      month = {},
      note = {},
      abstract = {},
      keywords = {},
      source = {},
      doi = {10.1017/jsl.2017.75},
      eprint = {1610.02729},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://jdh.hamkins.org/ord-is-not-definably-weakly-compact},
      }
  • The Vopěnka principle is inequivalent to but conservative over the Vopěnka scheme
    • J. D. Hamkins, “The Vopěnka principle is inequivalent to but conservative over the Vopěnka scheme,” ArXiv e-prints, 2016.
      [Bibtex]
      @ARTICLE{Hamkins:The-Vopenka-principle-is-inequivalent-to-but-conservative-over-the-Vopenka-scheme,
      author = {Joel David Hamkins},
      title = {The {Vop\v{e}nka} principle is inequivalent to but conservative over the {Vop\v{e}nka} scheme},
      journal = {ArXiv e-prints},
      year = {2016},
      volume = {},
      number = {},
      pages = {},
      month = {},
      note = {Under review},
      abstract = {},
      keywords = {under-review},
      source = {},
      eprint = {1606.03778},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://wp.me/p5M0LV-1lV},
      }
  • Set-theoretic mereology
    • [DOI] J. D. Hamkins and M. Kikuchi, “Set-theoretic mereology,” Logic and Logical Philosophy, Special issue “Mereology and beyond, part II”, vol. 25, iss. 3, p. 285–308, 2016.
      [Bibtex]
      @ARTICLE{HamkinsKikuchi2016:Set-theoreticMereology,
      author = {Joel David Hamkins and Makoto Kikuchi},
      title = {Set-theoretic mereology},
      journal = {Logic and Logical Philosophy, Special issue ``Mereology and beyond, part II''},
      editor = {A.~C.~Varzi and R.~Gruszczy{\'n}ski},
      year = {2016},
      volume = {25},
      number = {3},
      pages = {285--308},
      month = {},
      doi = {10.12775/LLP.2016.007},
      note = {},
      eprint = {1601.06593},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://jdh.hamkins.org/set-theoretic-mereology},
      abstract = {},
      keywords = {},
      source = {},
      ISSN = {1425-3305},
      MRCLASS = {03A05 (03E70)},
      MRNUMBER = {3546211},
      }
  • Upward closure and amalgamation in the generic multiverse of a countable model of set theory
    • J. D. Hamkins, “Upward closure and amalgamation in the generic multiverse of a countable model of set theory,” RIMS Kyôkyûroku, p. 17–31, 2016.
      [Bibtex]
      @ARTICLE{Hamkins2016:UpwardClosureAndAmalgamationInTheGenericMultiverse,
      author = {Joel David Hamkins},
      title = {Upward closure and amalgamation in the generic multiverse of a countable model of set theory},
      journal = {RIMS {Ky\^oky\^uroku}},
      year = {2016},
      volume = {},
      number = {},
      pages = {17--31},
      month = {},
      newton = {ni15066},
      url = {http://wp.me/p5M0LV-1cv},
      eprint = {1511.01074},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      abstract = {},
      keywords = {},
      source = {},
      issn = {1880-2818},
      }
  • A position in infinite chess with game value $\omega^4$
  • Open determinacy for class games
    • V. Gitman and J. D. Hamkins, “Open determinacy for class games,” in Foundations of Mathematics, Logic at Harvard, Essays in Honor of Hugh Woodin’s 60th Birthday, A. E. Caicedo, J. Cummings, P. Koellner, and P. Larson, Eds., , 2016, Newton Institute preprint ni15064.
      [Bibtex]
      @INCOLLECTION{GitmanHamkins2016:OpenDeterminacyForClassGames,
      author = {Victoria Gitman and Joel David Hamkins},
      title = {Open determinacy for class games},
      booktitle = {{Foundations of Mathematics, Logic at Harvard, Essays in Honor of Hugh Woodin's 60th Birthday}},
      publisher = {},
      year = {2016},
      editor = {Andr\'es E. Caicedo and James Cummings and Peter Koellner and Paul Larson},
      volume = {},
      number = {},
      series = {AMS Contemporary Mathematics},
      type = {},
      chapter = {},
      pages = {},
      address = {},
      edition = {},
      month = {},
      note = {Newton Institute preprint ni15064},
      url = {http://wp.me/p5M0LV-1af},
      eprint = {1509.01099},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      abstract = {},
      keywords = {},
      }
  • A mathematician’s year in Japan
    • J. D. Hamkins, A Mathematician’s Year in Japan, Amazon Kindle Direct Publishing, 2015, 156 pages.
      [Bibtex]
      @BOOK{Hamkins2015:AMathematiciansYearInJapan,
      author = {Joel David Hamkins},
      title = {A {Mathematician's} {Year} in {Japan}},
      publisher = {Amazon Kindle Direct Publishing},
      year = {2015},
      month = {March},
      keywords = {book},
      url = {http://www.amazon.com/dp/B00U618LM2},
      note = {156 pages},
      }
  • Ehrenfeucht’s lemma in set theory
    • [DOI] G. Fuchs, V. Gitman, and J. D. Hamkins, “Ehrenfeucht’s Lemma in Set Theory,” Notre Dame Journal of Formal Logic, vol. 59, iss. 3, p. 355–370, 2018.
      [Bibtex]
      @ARTICLE{FuchsGitmanHamkins2018:EhrenfeuchtsLemmaInSetTheory,
      author = "Fuchs, Gunter and Gitman, Victoria and Hamkins, Joel David",
      doi = "10.1215/00294527-2018-0007",
      fjournal = "Notre Dame Journal of Formal Logic",
      journal = "Notre Dame Journal of Formal Logic",
      number = "3",
      pages = "355--370",
      publisher = "Duke University Press",
      title = "Ehrenfeucht’s Lemma in Set Theory",
      volume = "59",
      year = "2018",
      eprint = {1501.01918},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://jdh.hamkins.org/ehrenfeuchts-lemma-in-set-theory},
      }
  • Incomparable $\omega_1$-like models of set theory
    • [DOI] G. Fuchs, V. Gitman, and J. D. Hamkins, “Incomparable $\omega_1$-like models of set theory,” Math.~Logic Q., p. 1–11, 2017.
      [Bibtex]
      @article {FuchsGitmanHamkins2017:IncomparableOmega1-likeModelsOfSetTheory,
      author = {Fuchs, Gunter and Gitman, Victoria and Hamkins, Joel David},
      title = {Incomparable $\omega_1$-like models of set theory},
      journal = {Math.~Logic Q.},
      issn = {1521-3870},
      doi = {10.1002/malq.201500002},
      pages = {1--11},
      year = {2017},
      month = {March},
      eprint = {1501.01022},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://jdh.hamkins.org/incomparable-omega-one-like-models-of-set-theory},
      }
  • Large cardinals need not be large in HOD
    • [DOI] Y. Cheng, S. Friedman, and J. D. Hamkins, “Large cardinals need not be large in HOD,” Annals of Pure and Applied Logic, vol. 166, iss. 11, pp. 1186-1198, 2015.
      [Bibtex]
      @ARTICLE{ChengFriedmanHamkins2015:LargeCardinalsNeedNotBeLargeInHOD,
      title = "Large cardinals need not be large in {HOD} ",
      journal = "Annals of Pure and Applied Logic ",
      volume = "166",
      number = "11",
      pages = "1186 - 1198",
      year = "2015",
      note = "",
      issn = "0168-0072",
      doi = "10.1016/j.apal.2015.07.004",
      eprint = {1407.6335},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://jdh.hamkins.org/large-cardinals-need-not-be-large-in-hod},
      author = "Yong Cheng and Sy-David Friedman and Joel David Hamkins",
      keywords = "Large cardinals",
      keywords = "HOD",
      keywords = "Forcing",
      keywords = "Absoluteness ",
      abstract = "Abstract We prove that large cardinals need not generally exhibit their large cardinal nature in HOD. For example, a supercompact cardinal κ need not be weakly compact in HOD, and there can be a proper class of supercompact cardinals in V, none of them weakly compact in HOD, with no supercompact cardinals in HOD. Similar results hold for many other types of large cardinals, such as measurable and strong cardinals.",
      }
  • Strongly uplifting cardinals and the boldface resurrection axioms
    • [DOI] J. D. Hamkins and T. Johnstone, “Strongly uplifting cardinals and the boldface resurrection axioms,” Archive for Mathematical Logic, vol. 56, iss. 7, p. 1115–1133, 2017.
      [Bibtex]
      @ARTICLE{HamkinsJohnstone2017:StronglyUpliftingCardinalsAndBoldfaceResurrection,
      author = {Joel David Hamkins and Thomas Johnstone},
      title = {Strongly uplifting cardinals and the boldface resurrection axioms},
      journal="Archive for Mathematical Logic",
      year="2017",
      month="Nov",
      day="01",
      volume="56",
      number="7",
      pages="1115--1133",
      eprint = {1403.2788},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      issn="1432-0665",
      doi="10.1007/s00153-017-0542-y",
      url = {http://wp.me/p5M0LV-IE},
      abstract="We introduce the strongly uplifting cardinals, which are equivalently characterized, we prove, as the superstrongly unfoldable cardinals and also as the almost-hugely unfoldable cardinals, and we show that their existence is equiconsistent over ZFC with natural instances of the boldface resurrection axiom, such as the boldface resurrection axiom for proper forcing.",
      keywords = {},
      source = {},
      }
  • Satisfaction is not absolute
    • J. D. Hamkins and R. Yang, “Satisfaction is not absolute,” to appear in the Review of Symbolic Logic, p. 1–34, 2014.
      [Bibtex]
      @ARTICLE{HamkinsYang:SatisfactionIsNotAbsolute,
      author = {Joel David Hamkins and Ruizhi Yang},
      title = {Satisfaction is not absolute},
      journal = {to appear in the Review of Symbolic Logic},
      year = {2014},
      volume = {},
      number = {},
      pages = {1--34},
      month = {},
      note = {},
      abstract = {},
      keywords = {to-appear},
      source = {},
      eprint = {1312.0670},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://wp.me/p5M0LV-Gf},
      doi = {},
      }
  • The foundation axiom and elementary self-embeddings of the universe
    • A. S. Daghighi, M. Golshani, J. Hamkins, and E. Jeřábek, “The foundation axiom and elementary self-embeddings of the universe,” in Infinity, Computability, and Metamathematics: Festschrift celebrating the 60th birthdays of Peter Koepke and Philip Welch, S. Geschke, B. Löwe, and P. Schlicht, Eds., College Publishers, 2014, vol. 23, p. 89–112.
      [Bibtex]
      @incollection {DaghighiGolshaniHaminsJerabek2013:TheFoundationAxiomAndElementarySelfEmbeddingsOfTheUniverse,
      AUTHOR = {Daghighi, Ali Sadegh and Golshani, Mohammad and Hamkins, Joel
      David and Je{\v{r}}{\'a}bek, Emil},
      TITLE = {The foundation axiom and elementary self-embeddings of the
      universe},
      BOOKTITLE = {{Infinity, Computability, and Metamathematics:
      Festschrift celebrating the 60th birthdays of Peter Koepke
      and Philip Welch}},
      SERIES = {Tributes},
      VOLUME = {23},
      PAGES = {89--112},
      PUBLISHER = {College Publishers},
      EDITOR = {S. Geschke and B. Löwe and P. Schlicht},
      YEAR = {2014},
      MRCLASS = {03E70 (03E30)},
      MRNUMBER = {3307881},
      eprint = {1311.0814},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://jdh.hamkins.org/the-role-of-foundation-in-the-kunen-inconsistency/},
      }
  • Resurrection axioms and uplifting cardinals
    • [DOI] J. D. Hamkins and T. Johnstone, “Resurrection axioms and uplifting cardinals,” Archive for Mathematical Logic, vol. 53, iss. 3-4, p. p.~463–485, 2014.
      [Bibtex]
      @ARTICLE{HamkinsJohnstone2014:ResurrectionAxiomsAndUpliftingCardinals,
      AUTHOR = "Joel David Hamkins and Thomas Johnstone",
      TITLE = "Resurrection axioms and uplifting cardinals",
      JOURNAL = "Archive for Mathematical Logic",
      publisher= {Springer},
      YEAR = "2014",
      volume = "53",
      number = "3-4",
      pages = "p.~463--485",
      month = "",
      note = "",
      url = "http://jdh.hamkins.org/resurrection-axioms-and-uplifting-cardinals",
      eprint = "1307.3602",
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      doi= "10.1007/s00153-014-0374-y",
      issn= {0933-5846},
      abstract = "",
      keywords = "",
      source = "",
      file = F,
      }
  • Superstrong and other large cardinals are never Laver indestructible
    • [DOI] J. Bagaria, J. D. Hamkins, K. Tsaprounis, and T. Usuba, “Superstrong and other large cardinals are never Laver indestructible,” Arch. Math. Logic, vol. 55, iss. 1-2, p. 19–35, 2016.
      [Bibtex]
      @ARTICLE{BagariaHamkinsTsaprounisUsuba2016:SuperstrongAndOtherLargeCardinalsAreNeverLaverIndestructible,
      AUTHOR = {Bagaria, Joan and Hamkins, Joel David and Tsaprounis,
      Konstantinos and Usuba, Toshimichi},
      TITLE = {Superstrong and other large cardinals are never {L}aver
      indestructible},
      JOURNAL = {Arch. Math. Logic},
      FJOURNAL = {Archive for Mathematical Logic},
      note = {Special volume in memory of R.~Laver},
      VOLUME = {55},
      YEAR = {2016},
      NUMBER = {1-2},
      PAGES = {19--35},
      ISSN = {0933-5846},
      MRCLASS = {03E55 (03E40)},
      MRNUMBER = {3453577},
      MRREVIEWER = {Peter Holy},
      DOI = {10.1007/s00153-015-0458-3},
      eprint = {1307.3486},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://jdh.hamkins.org/superstrong-never-indestructible/},
      }
  • The least weakly compact cardinal can be unfoldable, weakly measurable and nearly $\theta$-supercompact
    • [DOI] B. Cody, M. Gitik, J. D. Hamkins, and J. A. Schanker, “The least weakly compact cardinal can be unfoldable, weakly measurable and nearly $\theta$ supercompact,” Archive for Mathematical Logic, p. 1–20, 2015.
      [Bibtex]
      @article{CodyGitikHamkinsSchanker2015:LeastWeaklyCompact,
      year= {2015},
      issn= {0933-5846},
      journal= {Archive for Mathematical Logic},
      doi= {10.1007/s00153-015-0423-1},
      title= {The least weakly compact cardinal can be unfoldable, weakly measurable and nearly $\theta$ supercompact},
      publisher= {Springer},
      keywords= {Weakly compact; Unfoldable; Weakly measurable; Nearly supercompact; Identity crisis; Primary 03E55; 03E35},
      author= {Cody, Brent and Gitik, Moti and Hamkins, Joel David and Schanker, Jason A.},
      pages= {1--20},
      language= {English},
      eprint = {1305.5961},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url= {http://jdh.hamkins.org/least-weakly-compact},
      }
  • Algebraicity and implicit definability in set theory
    • [DOI] J. D. Hamkins and C. Leahy, “Algebraicity and Implicit Definability in Set Theory,” Notre Dame Journal of Formal Logic, vol. 57, iss. 3, p. 431–439, 2016.
      [Bibtex]
      @article{HamkinsLeahy2016:AlgebraicityAndImplicitDefinabilityInSetTheory,
      author = "Hamkins, Joel David and Leahy, Cole",
      doi = "10.1215/00294527-3542326",
      fjournal = "Notre Dame Journal of Formal Logic",
      journal = "Notre Dame Journal of Formal Logic",
      number = "3",
      pages = "431--439",
      publisher = "Duke University Press",
      title = "Algebraicity and Implicit Definability in Set Theory",
      volume = "57",
      year = "2016",
      url = {http://jdh.hamkins.org/algebraicity-and-implicit-definability},
      eprint = {1305.5953},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      ISSN = {0029-4527},
      MRCLASS = {03E47 (03C55)},
      MRNUMBER = {3521491},
      }
  • Transfinite game values in infinite chess
    • C.~D.~A.~Evans and J. D. Hamkins, “Transfinite game values in infinite chess,” Integers, vol. 14, p. Paper No.~G2, 36, 2014.
      [Bibtex]
      @ARTICLE{EvansHamkins2014:TransfiniteGameValuesInInfiniteChess,
      AUTHOR = {C.~D.~A.~Evans and Joel David Hamkins},
      TITLE = {Transfinite game values in infinite chess},
      JOURNAL = {Integers},
      FJOURNAL = {Integers Electronic Journal of Combinatorial Number Theory},
      YEAR = {2014},
      volume = {14},
      number = {},
      pages = {Paper No.~G2, 36},
      month = {},
      note = {},
      eprint = {1302.4377},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://jdh.hamkins.org/game-values-in-infinite-chess},
      ISSN = {1553-1732},
      MRCLASS = {03Exx (91A46)},
      MRNUMBER = {3225916},
      abstract = {},
      keywords = {},
      source = {},
      }
  • A multiverse perspective on the axiom of constructiblity
    • [DOI] J. D. Hamkins, “A multiverse perspective on the axiom of constructibility,” in Infinity and Truth, World Sci. Publ., Hackensack, NJ, 2014, vol. 25, p. 25–45.
      [Bibtex]
      @incollection {Hamkins2014:MultiverseOnVeqL,
      AUTHOR = {Hamkins, Joel David},
      TITLE = {A multiverse perspective on the axiom of constructibility},
      BOOKTITLE = {{Infinity and Truth}},
      SERIES = {LNS Math Natl. Univ. Singap.},
      VOLUME = {25},
      PAGES = {25--45},
      PUBLISHER = {World Sci. Publ., Hackensack, NJ},
      YEAR = {2014},
      MRCLASS = {03E45 (03A05)},
      MRNUMBER = {3205072},
      DOI = {10.1142/9789814571043_0002},
      url = {http://wp.me/p5M0LV-qE},
      eprint = {1210.6541},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      }
  • A question for the mathematics oracle

    At the Workshop on Infinity and Truth in Singapore last year, we had a special session in which the speakers were asked to imagine that they had been granted an audience with an all-knowing mathematical oracle, given the opportunity to ask …

  • Moving up and down in the generic multiverse
    • [DOI] J. D. Hamkins and B. Löwe, “Moving up and down in the generic multiverse,” Logic and its Applications, ICLA 2013 LNCS, vol. 7750, p. 139–147, 2013.
      [Bibtex]
      @ARTICLE{HamkinsLoewe2013:MovingUpAndDownInTheGenericMultiverse,
      AUTHOR = {Joel David Hamkins and Benedikt Löwe},
      title = {Moving up and down in the generic multiverse},
      journal = {Logic and its Applications, ICLA 2013 LNCS},
      publisher= {Springer},
      editor= {Lodaya, Kamal},
      isbn= {978-3-642-36038-1},
      year = {2013},
      volume = {7750},
      number = {},
      pages = {139--147},
      doi= {10.1007/978-3-642-36039-8_13},
      month = {},
      note = {},
      url = {http://wp.me/p5M0LV-od},
      eprint = {1208.5061},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      abstract = {},
      keywords = {},
      source = {},
      }
  • Structural connections between a forcing class and its modal logic
    • [DOI] J. D. Hamkins, G. Leibman, and B. Löwe, “Structural connections between a forcing class and its modal logic,” Israel Journal of Mathematics, vol. 207, iss. 2, p. 617–651, 2015.
      [Bibtex]
      @article {HamkinsLeibmanLoewe2015:StructuralConnectionsForcingClassAndItsModalLogic,
      AUTHOR = {Hamkins, Joel David and Leibman, George and Löwe,
      Benedikt},
      TITLE = {Structural connections between a forcing class and its modal
      logic},
      JOURNAL = {Israel Journal of Mathematics},
      FJOURNAL = {Israel Journal of Mathematics},
      VOLUME = {207},
      YEAR = {2015},
      NUMBER = {2},
      PAGES = {617--651},
      ISSN = {0021-2172},
      MRCLASS = {03E40 (03B45)},
      MRNUMBER = {3359713},
      DOI = {10.1007/s11856-015-1185-5},
      url = {http://wp.me/p5M0LV-kf},
      eprint = {1207.5841},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      }
  • Every countable model of set theory embeds into its own constructible universe
    • [DOI] J. D. Hamkins, “Every countable model of set theory embeds into its own constructible universe,” Journal of Mathematical Logic, vol. 13, iss. 2, p. 1350006, 27, 2013.
      [Bibtex]
      @article {Hamkins2013:EveryCountableModelOfSetTheoryEmbedsIntoItsOwnL,
      AUTHOR = {Hamkins, Joel David},
      TITLE = {Every countable model of set theory embeds into its own
      constructible universe},
      JOURNAL = {Journal of Mathematical Logic},
      VOLUME = {13},
      YEAR = {2013},
      NUMBER = {2},
      PAGES = {1350006, 27},
      ISSN = {0219-0613},
      MRCLASS = {03C62 (03E99 05C20 05C60 05C63)},
      MRNUMBER = {3125902},
      MRREVIEWER = {Robert S. Lubarsky},
      DOI = {10.1142/S0219061313500062},
      eprint = {1207.0963},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      URL = {http://wp.me/p5M0LV-jn},
      }
  • Well-founded Boolean ultrapowers as large cardinal embeddings
    • J. D. Hamkins and D. Seabold, “Well-founded Boolean ultrapowers as large cardinal embeddings,” , p. 1–40, 2006.
      [Bibtex]
      @ARTICLE{HamkinsSeabold:BooleanUltrapowers,
      AUTHOR = "Joel David Hamkins and Daniel Seabold",
      TITLE = "Well-founded {Boolean} ultrapowers as large cardinal embeddings",
      JOURNAL = "",
      YEAR = "2006",
      volume = "",
      number = "",
      pages = "1--40",
      month = "",
      note = "",
      eprint = "1206.6075",
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://jdh.hamkins.org/boolean-ultrapowers/},
      abstract = "",
      keywords = "",
      source = "",
      file = F,
      }
  • Singular cardinals and strong extenders
    • [DOI] A. W. Apter, J. Cummings, and J. D. Hamkins, “Singular cardinals and strong extenders,” Central European Journal of Mathematics, vol. 11, iss. 9, p. 1628–1634, 2013.
      [Bibtex]
      @article {ApterCummingsHamkins2013:SingularCardinalsAndStrongExtenders,
      AUTHOR = {Apter, Arthur W. and Cummings, James and Hamkins, Joel David},
      TITLE = {Singular cardinals and strong extenders},
      JOURNAL = {Central European Journal of Mathematics},
      VOLUME = {11},
      YEAR = {2013},
      NUMBER = {9},
      PAGES = {1628--1634},
      ISSN = {1895-1074},
      MRCLASS = {03E55 (03E35 03E45)},
      MRNUMBER = {3071929},
      MRREVIEWER = {Samuel Gomes da Silva},
      DOI = {10.2478/s11533-013-0265-1},
      URL = {http://jdh.hamkins.org/singular-cardinals-strong-extenders/},
      eprint = {1206.3703},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      }
  • Is the dream solution of the continuum hypothesis attainable?
    • [DOI] J. D. Hamkins, “Is the dream solution of the continuum hypothesis attainable?,” Notre Dame Journal of Formal Logic, vol. 56, iss. 1, p. 135–145, 2015.
      [Bibtex]
      @article {Hamkins2015:IsTheDreamSolutionToTheContinuumHypothesisAttainable,
      AUTHOR = {Hamkins, Joel David},
      TITLE = {Is the dream solution of the continuum hypothesis attainable?},
      JOURNAL = {Notre Dame Journal of Formal Logic},
      FJOURNAL = {Notre Dame Journal of Formal Logic},
      VOLUME = {56},
      YEAR = {2015},
      NUMBER = {1},
      PAGES = {135--145},
      ISSN = {0029-4527},
      MRCLASS = {03E50},
      MRNUMBER = {3326592},
      MRREVIEWER = {Marek Balcerzak},
      DOI = {10.1215/00294527-2835047},
      eprint = {1203.4026},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://jdh.hamkins.org/dream-solution-of-ch},
      }
  • The mate-in-n problem of infinite chess is decidable
    • [DOI] D. Brumleve, J. D. Hamkins, and P. Schlicht, “The Mate-in-$n$ Problem of Infinite Chess Is Decidable,” in How the World Computes, S. Cooper, A. Dawar, and B. Löwe, Eds., Springer, 2012, vol. 7318, pp. 78-88.
      [Bibtex]
      @incollection{BrumleveHamkinsSchlicht2012:TheMateInNProblemOfInfiniteChessIsDecidable,
      year= {2012},
      isbn= {978-3-642-30869-7},
      booktitle= {{How the World Computes}},
      volume= {7318},
      series= {Lecture Notes in Computer Science},
      editor= {Cooper, S.~Barry and Dawar, Anuj and Löwe, Benedikt},
      doi= {10.1007/978-3-642-30870-3_9},
      title= {The Mate-in-$n$ Problem of Infinite Chess Is Decidable},
      url= {http://wp.me/p5M0LV-f8},
      publisher= {Springer},
      author= {Brumleve, Dan and Hamkins, Joel David and Schlicht, Philipp},
      pages= {78-88},
      eprint = {1201.5597},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      }
  • Inner models with large cardinal features usually obtained by forcing
    • [DOI] A. W.~Apter, V. Gitman, and J. D. Hamkins, “Inner models with large cardinal features usually obtained by forcing,” Archive for Math.~Logic, vol. 51, p. 257–283, 2012.
      [Bibtex]
      @article {ApterGitmanHamkins2012:InnerModelsWithLargeCardinals,
      author = {Arthur W.~Apter and Victoria Gitman and Joel David Hamkins},
      affiliation = {Mathematics, The Graduate Center of the City University of New York, 365 Fifth Avenue, New York, NY 10016, USA},
      title = {Inner models with large cardinal features usually obtained by forcing},
      journal = {Archive for Math.~Logic},
      publisher = {Springer},
      issn = {0933-5846},
      keyword = {},
      pages = {257--283},
      volume = {51},
      issue = {3},
      url = {http://jdh.hamkins.org/innermodels},
      eprint = {1111.0856},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      doi = {10.1007/s00153-011-0264-5},
      note = {},
      year = {2012},
      }
  • What is the theory ZFC without power set?
    • [DOI] V. Gitman, J. D. Hamkins, and T. A.~Johnstone, “What is the theory ZFC without Powerset?,” Math.~Logic Q., vol. 62, iss. 4–5, p. 391–406, 2016.
      [Bibtex]
      @ARTICLE{GitmanHamkinsJohnstone2016:WhatIsTheTheoryZFC-Powerset?,
      AUTHOR = {Victoria Gitman and Joel David Hamkins and Thomas A.~Johnstone},
      TITLE = {What is the theory {ZFC} without {Powerset}?},
      JOURNAL = {Math.~Logic Q.},
      YEAR = {2016},
      volume = {62},
      number = {4--5},
      pages = {391--406},
      month = {},
      note = {},
      abstract = {},
      keywords = {},
      doi = {10.1002/malq.201500019},
      eprint = {1110.2430},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://jdh.hamkins.org/what-is-the-theory-zfc-without-power-set},
      source = {},
      ISSN = {0942-5616},
      MRCLASS = {03E30},
      MRNUMBER = {3549557},
      MRREVIEWER = {Arnold W. Miller},
      }
  • The hierarchy of equivalence relations on the natural numbers under computable reducibility
    • [DOI] S. Coskey, J. D. Hamkins, and R. Miller, “The hierarchy of equivalence relations on the natural numbers under computable reducibility,” Computability, vol. 1, iss. 1, p. 15–38, 2012.
      [Bibtex]
      @ARTICLE{CoskeyHamkinsMiller2012:HierarchyOfEquivalenceRelationsOnN,
      AUTHOR = {Samuel Coskey and Joel David Hamkins and Russell Miller},
      TITLE = {The hierarchy of equivalence relations on the natural numbers under computable reducibility},
      JOURNAL = {Computability},
      YEAR = {2012},
      volume = {1},
      number = {1},
      pages = {15--38},
      month = {},
      note = {},
      url = {http://jdh.hamkins.org/equivalence-relations-on-naturals/},
      eprint = {1109.3375},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      doi = {10.3233/COM-2012-004},
      abstract = {},
      keywords = {},
      source = {},
      }
  • Set-theoretic geology
    • [DOI] G. Fuchs, J. D. Hamkins, and J. Reitz, “Set-theoretic geology,” Annals of Pure and Applied Logic, vol. 166, iss. 4, p. 464–501, 2015.
      [Bibtex]
      @article{FuchsHamkinsReitz2015:Set-theoreticGeology,
      author = "Gunter Fuchs and Joel David Hamkins and Jonas Reitz",
      title = "Set-theoretic geology",
      journal = "Annals of Pure and Applied Logic",
      volume = "166",
      number = "4",
      pages = "464--501",
      year = "2015",
      note = "",
      MRCLASS = {03E55 (03E40 03E45 03E47)},
      MRNUMBER = {3304634},
      issn = "0168-0072",
      doi = "10.1016/j.apal.2014.11.004",
      eprint = "1107.4776",
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = "http://jdh.hamkins.org/set-theoreticgeology",
      }
  • The rigid relation principle, a new weak choice principle
    • [DOI] J. D. Hamkins and J. Palumbo, “The rigid relation principle, a new weak choice principle,” Mathematical Logic Quarterly, vol. 58, iss. 6, p. 394–398, 2012.
      [Bibtex]
      @ARTICLE{HamkinsPalumbo2012:TheRigidRelationPrincipleANewWeakACPrinciple,
      AUTHOR = {Joel David Hamkins and Justin Palumbo},
      TITLE = {The rigid relation principle, a new weak choice principle},
      JOURNAL = {Mathematical Logic Quarterly},
      YEAR = {2012},
      volume = {58},
      number = {6},
      pages = {394--398},
      ISSN = {0942-5616},
      month = {},
      note = {},
      url = {http://jdh.hamkins.org/rigid-relation-principle/},
      eprint = {1106.4635},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      doi = {10.1002/malq.201100081},
      MRNUMBER = {2997028},
      MRREVIEWER = {Eleftherios C.~Tachtsis},
      abstract = {},
      keywords = {},
      source = {},
      }
  • Generalizations of the Kunen inconsistency
    • [DOI] J. D. Hamkins, G. Kirmayer, and N. L. Perlmutter, “Generalizations of the Kunen inconsistency,” Annals of Pure and Applied Logic, vol. 163, iss. 12, pp. 1872-1890, 2012.
      [Bibtex]
      @article{HamkinsKirmayerPerlmutter2012:GeneralizationsOfKunenInconsistency,
      title = "Generalizations of the {Kunen} inconsistency",
      journal = "Annals of Pure and Applied Logic",
      volume = "163",
      number = "12",
      pages = "1872 - 1890",
      year = "2012",
      note = "",
      issn = "0168-0072",
      doi = "10.1016/j.apal.2012.06.001",
      eprint = {1106.1951},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = "http://jdh.hamkins.org/generalizationsofkuneninconsistency",
      author = "Joel David Hamkins and Greg Kirmayer and Norman Lewis Perlmutter",
      }
  • Pointwise definable models of set theory
    • [DOI] J. D. Hamkins, D. Linetsky, and J. Reitz, “Pointwise definable models of set theory,” Journal of Symbolic Logic, vol. 78, iss. 1, p. 139–156, 2013.
      [Bibtex]
      @article {HamkinsLinetskyReitz2013:PointwiseDefinableModelsOfSetTheory,
      AUTHOR = {Hamkins, Joel David and Linetsky, David and Reitz, Jonas},
      TITLE = {Pointwise definable models of set theory},
      JOURNAL = {Journal of Symbolic Logic},
      FJOURNAL = {Journal of Symbolic Logic},
      VOLUME = {78},
      YEAR = {2013},
      NUMBER = {1},
      PAGES = {139--156},
      ISSN = {0022-4812},
      MRCLASS = {03E55},
      MRNUMBER = {3087066},
      MRREVIEWER = {Bernhard A. König},
      DOI = {10.2178/jsl.7801090},
      URL = {http://jdh.hamkins.org/pointwisedefinablemodelsofsettheory/},
      eprint = "1105.4597",
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      }
  • Effective Mathemematics of the Uncountable
    • Effective Mathematics of the Uncountable, N.~Greenberg, J.~D.~Hamkins, D.~R.~Hirschfeldt, and R.~G.~Miller, Eds., Cambridge University Press, ASL Lecture Notes in Logic, 2013, vol. 41.
      [Bibtex]
      @BOOK{EMU,
      AUTHOR = {},
      editor = {N.~Greenberg and J.~D.~Hamkins and D.~R.~Hirschfeldt and R.~G.~Miller},
      TITLE = {{Effective Mathematics of the Uncountable}},
      PUBLISHER = {Cambridge University Press, ASL Lecture Notes in Logic},
      YEAR = {2013},
      volume = {41},
      number = {},
      series = {},
      address = {},
      edition = {},
      month = {},
      note = {},
      abstract = {},
      isbn = {9781107014510},
      price = {},
      keywords = {book,edited-volume},
      url = {http://wp.me/s5M0LV-emu},
      source = {},
      }
  • Infinite time Turing machines and an application to the hierarchy of equivalence relations on the reals
    • S. Coskey and J. D. Hamkins, “Infinite time Turing machines and an application to the hierarchy of equivalence relations on the reals,” in Effective Mathematics of the Uncountable, Assoc. Symbol. Logic, La Jolla, CA, 2013, vol. 41, p. 33–49.
      [Bibtex]
      @incollection {CoskeyHamkins2013:ITTMandApplicationsToEquivRelations,
      AUTHOR = {Coskey, Samuel and Hamkins, Joel David},
      TITLE = {Infinite time {T}uring machines and an application to the
      hierarchy of equivalence relations on the reals},
      BOOKTITLE = {{Effective Mathematics of the Uncountable}},
      SERIES = {Lect. Notes Log.},
      VOLUME = {41},
      PAGES = {33--49},
      PUBLISHER = {Assoc. Symbol. Logic, La Jolla, CA},
      YEAR = {2013},
      MRCLASS = {03D30 (03D60 03E15)},
      MRNUMBER = {3205053},
      eprint = {1101.1864},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://jdh.hamkins.org/ittms-and-applications/},
      }
  • The set-theoretical multiverse
    • [DOI] J. D. Hamkins, “The set-theoretic multiverse,” Review of Symbolic Logic, vol. 5, p. 416–449, 2012.
      [Bibtex]
      @ARTICLE{Hamkins2012:TheSet-TheoreticalMultiverse,
      AUTHOR = {Joel David Hamkins},
      TITLE = {The set-theoretic multiverse},
      JOURNAL = {Review of Symbolic Logic},
      YEAR = {2012},
      volume = {5},
      number = {},
      pages = {416--449},
      month = {},
      note = {},
      url = {http://jdh.hamkins.org/themultiverse},
      doi = {10.1017/S1755020311000359},
      abstract = {},
      keywords = {},
      source = {},
      eprint = {1108.4223},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      }
  • Infinite time decidable equivalence relation theory
    • [DOI] S. Coskey and J. D. Hamkins, “Infinite time decidable equivalence relation theory,” Notre Dame Journal of Formal Logic, vol. 52, iss. 2, p. 203–228, 2011.
      [Bibtex]
      @ARTICLE{CoskeyHamkins2011:InfiniteTimeComputableEquivalenceRelations,
      AUTHOR = {Coskey, Samuel and Hamkins, Joel David},
      TITLE = {Infinite time decidable equivalence relation theory},
      JOURNAL = {Notre Dame Journal of Formal Logic},
      FJOURNAL = {Notre Dame Journal of Formal Logic},
      VOLUME = {52},
      YEAR = {2011},
      NUMBER = {2},
      PAGES = {203--228},
      ISSN = {0029-4527},
      MRCLASS = {03D65 (03D30 03E15)},
      MRNUMBER = {2794652},
      DOI = {10.1215/00294527-1306199},
      URL = {http://wp.me/p5M0LV-3M},
      eprint = "0910.4616",
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      }
  • The set-theoretical multiverse: a natural context for set theory, Japan 2009
    • [DOI] J. D. Hamkins, “The Set-theoretic Multiverse : A Natural Context for Set Theory,” Annals of the Japan Association for Philosophy of Science, vol. 19, p. 37–55, 2011.
      [Bibtex]
      @article{Hamkins2011:TheMultiverse:ANaturalContext,
      author="Joel David Hamkins",
      title="The Set-theoretic Multiverse : A Natural Context for Set Theory",
      journal="Annals of the Japan Association for Philosophy of Science",
      ISSN="0453-0691",
      publisher="the Japan Association for Philosophy of Science",
      year="2011",
      volume="19",
      number="",
      pages="37--55",
      URL="http://jdh.hamkins.org/themultiverseanaturalcontext",
      doi={10.4288/jafpos.19.0_37},
      }
  • A natural model of the multiverse axioms
    • [DOI] V. Gitman and J. D. Hamkins, “A natural model of the multiverse axioms,” Notre Dame Journal of Formal Logic, vol. 51, iss. 4, p. 475–484, 2010.
      [Bibtex]
      @ARTICLE{GitmanHamkins2010:NaturalModelOfMultiverseAxioms,
      AUTHOR = {Gitman, Victoria and Hamkins, Joel David},
      TITLE = {A natural model of the multiverse axioms},
      JOURNAL = {Notre Dame Journal of Formal Logic},
      FJOURNAL = {Notre Dame Journal of Formal Logic},
      VOLUME = {51},
      YEAR = {2010},
      NUMBER = {4},
      PAGES = {475--484},
      ISSN = {0029-4527},
      MRCLASS = {03E40},
      MRNUMBER = {2741838},
      DOI = {10.1215/00294527-2010-030},
      URL = {http://wp.me/p5M0LV-3I},
      eprint = {1104.4450},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      }
  • Indestructible strong unfoldability
    • [DOI] J. D. Hamkins and T. A. Johnstone, “Indestructible strong unfoldability,” Notre Dame Journal of Formal Logic, vol. 51, iss. 3, p. 291–321, 2010.
      [Bibtex]
      @ARTICLE{HamkinsJohnstone2010:IndestructibleStrongUnfoldability,
      AUTHOR = {Hamkins, Joel David and Johnstone, Thomas A.},
      TITLE = {Indestructible strong unfoldability},
      JOURNAL = {Notre Dame Journal of Formal Logic},
      FJOURNAL = {Notre Dame Journal of Formal Logic},
      VOLUME = {51},
      YEAR = {2010},
      NUMBER = {3},
      PAGES = {291--321},
      ISSN = {0029-4527},
      MRCLASS = {03E55 (03E40)},
      MRNUMBER = {2675684 (2011i:03050)},
      MRREVIEWER = {Bernhard A. König},
      DOI = {10.1215/00294527-2010-018},
      URL = {http://jdh.hamkins.org/indestructiblestrongunfoldability/},
      file = F,
      }
  • Some second order set theory
    • [DOI] J. D. Hamkins, “Some second order set theory,” in Logic and its Applications, R.~Ramanujam and S.~Sarukkai, Eds., Springer, 2009, vol. 5378, p. 36–50.
      [Bibtex]
      @INCOLLECTION{Hamkins2009:SomeSecondOrderSetTheory,
      AUTHOR = {Hamkins, Joel David},
      TITLE = {Some second order set theory},
      BOOKTITLE = {{Logic and its Applications}},
      SERIES = {Lecture Notes in Comput.~Sci.},
      VOLUME = {5378},
      PAGES = {36--50},
      PUBLISHER = {Springer},
      EDITOR = {R.~Ramanujam and S.~Sarukkai},
      ADDRESS = {},
      YEAR = {2009},
      MRCLASS = {03E35 (03B45 03E40)},
      MRNUMBER = {2540935 (2011a:03053)},
      DOI = {10.1007/978-3-540-92701-3_3},
      URL = {http://wp.me/p5M0LV-3E},
      }
  • Post's problem for ordinal register machines: an explicit approach
    • [DOI] J. D. Hamkins and R. G. Miller, “Post’s problem for ordinal register machines: an explicit approach,” Ann.~Pure Appl.~Logic, vol. 160, iss. 3, p. 302–309, 2009.
      [Bibtex]
      @ARTICLE{HamkinsMiller2009:PostsProblemForORMsExplicitApproach,
      AUTHOR = {Hamkins, Joel David and Miller, Russell G.},
      TITLE = {Post's problem for ordinal register machines: an explicit approach},
      JOURNAL = {Ann.~Pure Appl.~Logic},
      FJOURNAL = {Annals of Pure and Applied Logic},
      VOLUME = {160},
      YEAR = {2009},
      NUMBER = {3},
      PAGES = {302--309},
      ISSN = {0168-0072},
      CODEN = {APALD7},
      MRCLASS = {03D60 (03D10)},
      MRNUMBER = {2555781 (2010m:03086)},
      MRREVIEWER = {Robert S.~Lubarsky},
      DOI = {10.1016/j.apal.2009.01.004},
      URL = {http://wp.me/p5M0LV-3C},
      file = F,
      }
  • Degrees of rigidity for Souslin trees
    • [DOI] G. Fuchs and J. D. Hamkins, “Degrees of rigidity for Souslin trees,” Journal of Symbolic Logic, vol. 74, iss. 2, p. 423–454, 2009.
      [Bibtex]
      @ARTICLE{FuchsHamkins2009:DegreesOfRigidity,
      AUTHOR = {Fuchs, Gunter and Hamkins, Joel David},
      TITLE = {Degrees of rigidity for {S}ouslin trees},
      JOURNAL = {Journal of Symbolic Logic},
      FJOURNAL = {Journal of Symbolic Logic},
      VOLUME = {74},
      YEAR = {2009},
      NUMBER = {2},
      PAGES = {423--454},
      ISSN = {0022-4812},
      CODEN = {JSYLA6},
      MRCLASS = {03E05},
      MRNUMBER = {2518565 (2010i:03049)},
      MRREVIEWER = {Stefan Geschke},
      URL = {http://wp.me/p5M0LV-3A},
      doi = {10.2178/jsl/1243948321},
      eprint = {math/0602482},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      file = F,
      }
  • Tall cardinals
    • [DOI] J. D. Hamkins, “Tall cardinals,” Math.~Logic Q., vol. 55, iss. 1, p. 68–86, 2009.
      [Bibtex]
      @ARTICLE{Hamkins2009:TallCardinals,
      AUTHOR = {Hamkins, Joel D.},
      TITLE = {Tall cardinals},
      JOURNAL = {Math.~Logic Q.},
      FJOURNAL = {Mathematical Logic Quarterly},
      VOLUME = {55},
      YEAR = {2009},
      NUMBER = {1},
      PAGES = {68--86},
      ISSN = {0942-5616},
      MRCLASS = {03E55 (03E35)},
      MRNUMBER = {2489293 (2010g:03083)},
      MRREVIEWER = {Carlos A.~Di Prisco},
      DOI = {10.1002/malq.200710084},
      URL = {http://wp.me/p5M0LV-3y},
      file = F,
      }
  • The proper and semi-proper forcing axioms for forcing notions that preserve $\aleph_2$ or $\aleph_3$
    • [DOI] J. D. Hamkins and T. A. Johnstone, “The proper and semi-proper forcing axioms for forcing notions that preserve $\aleph_2$ or $\aleph_3$,” Proc.~Amer.~Math.~Soc., vol. 137, iss. 5, p. 1823–1833, 2009.
      [Bibtex]
      @ARTICLE{HamkinsJohnstone2009:PFA(aleph_2-preserving),
      AUTHOR = {Hamkins, Joel David and Johnstone, Thomas A.},
      TITLE = {The proper and semi-proper forcing axioms for forcing notions that preserve {$\aleph_2$} or {$\aleph_3$}},
      JOURNAL = {Proc.~Amer.~Math.~Soc.},
      FJOURNAL = {Proceedings of the American Mathematical Society},
      VOLUME = {137},
      YEAR = {2009},
      NUMBER = {5},
      PAGES = {1823--1833},
      ISSN = {0002-9939},
      CODEN = {PAMYAR},
      MRCLASS = {03E55 (03E40)},
      MRNUMBER = {2470843 (2009k:03087)},
      MRREVIEWER = {John Krueger},
      DOI = {10.1090/S0002-9939-08-09727-X},
      URL = {http://wp.me/p5M0LV-3v},
      file = F,
      }
  • Infinite time computable model theory
    • J. D. Hamkins, R. Miller, D. Seabold, and S. Warner, “Infinite time computable model theory,” in New Computational Paradigms: Changing Conceptions of What is Computable, S. B. Cooper, B. Löwe, and A. Sorbi, Eds., Springer, 2008, p. 521–557.
      [Bibtex]
      @INCOLLECTION{HamkinsMillerSeaboldWarner2007:InfiniteTimeComputableModelTheory,
      AUTHOR = {Hamkins, Joel David and Miller, Russell and Seabold, Daniel
      and Warner, Steve},
      TITLE = {Infinite time computable model theory},
      BOOKTITLE = "{New Computational Paradigms: Changing Conceptions of What is Computable}",
      PAGES = {521--557},
      PUBLISHER = {Springer},
      ADDRESS = {},
      YEAR = {2008},
      MRCLASS = {03C57 (03D10)},
      MRNUMBER = {2762096},
      editor = {S. B. Cooper and Benedikt Löwe and Andrea Sorbi},
      isbn = "0-387-36033-6",
      file = F,
      url = {http://wp.me/p5M0LV-3t},
      }
  • Changing the heights of automorphism towers by forcing with Souslin trees over $L$
    • [DOI] G. Fuchs and J. D. Hamkins, “Changing the heights of automorphism towers by forcing with Souslin trees over $L$,” Journal of Symbolic Logic, vol. 73, iss. 2, p. 614–633, 2008.
      [Bibtex]
      @ARTICLE{FuchsHamkins2008:ChangingHeightsOverL,
      AUTHOR = {Fuchs, Gunter and Hamkins, Joel David},
      TITLE = {Changing the heights of automorphism towers by forcing with {S}ouslin trees over {$L$}},
      JOURNAL = {Journal of Symbolic Logic},
      VOLUME = {73},
      YEAR = {2008},
      NUMBER = {2},
      PAGES = {614--633},
      ISSN = {0022-4812},
      CODEN = {JSYLA6},
      MRCLASS = {03E35},
      MRNUMBER = {2414468 (2009e:03094)},
      MRREVIEWER = {Lutz Struengmann},
      URL = {http://wp.me/p5M0LV-3l},
      doi = {10.2178/jsl/1208359063},
      eprint = {math/0702768},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      file = F,
      }
  • The ground axiom is consistent with $V\ne{\rm HOD}$
    • [DOI] J. D. Hamkins, J. Reitz, and W. Woodin, “The ground axiom is consistent with $V\ne{\rm HOD}$,” Proc.~Amer.~Math.~Soc., vol. 136, iss. 8, p. 2943–2949, 2008.
      [Bibtex]
      @ARTICLE{HamkinsReitzWoodin2008:TheGroundAxiomAndVequalsHOD,
      AUTHOR = {Hamkins, Joel David and Reitz, Jonas and Woodin, W.~Hugh},
      TITLE = {The ground axiom is consistent with {$V\ne{\rm HOD}$}},
      JOURNAL = {Proc.~Amer.~Math.~Soc.},
      FJOURNAL = {Proceedings of the American Mathematical Society},
      VOLUME = {136},
      YEAR = {2008},
      NUMBER = {8},
      PAGES = {2943--2949},
      ISSN = {0002-9939},
      CODEN = {PAMYAR},
      MRCLASS = {03E35 (03E45 03E55)},
      MRNUMBER = {2399062 (2009b:03137)},
      MRREVIEWER = {P{\'e}ter Komj{\'a}th},
      DOI = {10.1090/S0002-9939-08-09285-X},
      URL = {http://wp.me/p5M0LV-3j},
      file = F,
      }
  • The modal logic of forcing
    • [DOI] J. D. Hamkins and B. Löwe, “The modal logic of forcing,” Trans.~AMS, vol. 360, iss. 4, p. 1793–1817, 2008.
      [Bibtex]
      @ARTICLE{HamkinsLoewe2008:TheModalLogicOfForcing,
      AUTHOR = {Hamkins, Joel David and Löwe, Benedikt},
      TITLE = {The modal logic of forcing},
      JOURNAL = {Trans.~AMS},
      FJOURNAL = {Transactions of the American Mathematical Society},
      VOLUME = {360},
      YEAR = {2008},
      NUMBER = {4},
      PAGES = {1793--1817},
      ISSN = {0002-9947},
      CODEN = {TAMTAM},
      MRCLASS = {03E40 (03B45)},
      MRNUMBER = {2366963 (2009h:03068)},
      MRREVIEWER = {Andreas Blass},
      DOI = {10.1090/S0002-9947-07-04297-3},
      URL = {http://wp.me/p5M0LV-3h},
      eprint = {math/0509616},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      }
  • Large cardinals with few measures
    • [DOI] A. W.~Apter, J. Cummings, and J. D. Hamkins, “Large cardinals with few measures,” Proc.~Amer.~Math.~Soc., vol. 135, iss. 7, p. 2291–2300, 2007.
      [Bibtex]
      @ARTICLE{ApterCummingsHamkins2006:LargeCardinalsWithFewMeasures,
      AUTHOR = {Arthur W.~Apter and James Cummings and Joel David Hamkins},
      TITLE = {Large cardinals with few measures},
      JOURNAL = {Proc.~Amer.~Math.~Soc.},
      FJOURNAL = {Proceedings of the American Mathematical Society},
      VOLUME = {135},
      YEAR = {2007},
      NUMBER = {7},
      PAGES = {2291--2300},
      ISSN = {0002-9939},
      CODEN = {PAMYAR},
      MRCLASS = {03E35 (03E55)},
      MRNUMBER = {2299507 (2008b:03067)},
      MRREVIEWER = {Tetsuya Ishiu},
      DOI = {10.1090/S0002-9939-07-08786-2},
      URL = {http://jdh.hamkins.org/largecardinalswithfewmeasures/},
      eprint = {math/0603260},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      file = F,
      }
  • A survey of infinite time Turing machines
    • [DOI] J. D. Hamkins, “A Survey of Infinite Time Turing Machines,” in Machines, Computations, and Universality – 5th International Conference MCU 2007, Orleans, France, 2007, p. 62–71.
      [Bibtex]
      @INPROCEEDINGS{Hamkins2007:ASurveyOfInfiniteTimeTuringMachines,
      AUTHOR = "Joel David Hamkins",
      TITLE = "A Survey of Infinite Time {T}uring Machines",
      BOOKTITLE = "{Machines, Computations, and Universality - 5th International Conference MCU 2007}",
      YEAR = "2007",
      editor = "{J\'er\^ ome} Durand-Lose and Maurice Margenstern",
      volume = "4664",
      number = "",
      series = "Lecture Notes in Computer Science",
      pages = "62--71",
      address = "Orleans, France",
      month = "",
      organization = "",
      publisher = "",
      note = "",
      abstract = "",
      keywords = "",
      doi = {10.1007/978-3-540-74593-8_5},
      file = F,
      url = {http://wp.me/p5M0LV-3d},
      }
  • The complexity of quickly decidable ORM-decidable sets
    • [DOI] J. D. Hamkins, D. Linetsky, and R. Miller, “The Complexity of Quickly Decidable ORM-Decidable Sets,” in Computation and Logic in the Real World – CiE 2007, Siena, Italy, 2007, p. 488–496.
      [Bibtex]
      @INPROCEEDINGS{HamkinsLinetskyMiller2007:ComplexityOfQuicklyDecidableORMSets,
      AUTHOR = "Joel David Hamkins and David Linetsky and Russell Miller",
      TITLE = "The Complexity of Quickly Decidable {ORM}-Decidable Sets",
      BOOKTITLE = "{Computation and Logic in the Real World - CiE 2007}",
      YEAR = "2007",
      editor = "B. Cooper and B. Löwe and A.~Sorbi",
      volume = "4497",
      number = "",
      series = "Proc.~LNCS",
      pages = "488--496",
      address = "Siena, Italy",
      month = "",
      organization = "",
      publisher = "",
      note = "",
      abstract = "",
      keywords = "",
      doi = {10.1007/978-3-540-73001-9_51},
      ee = {},
      bibsource = {DBLP, http://dblp.uni-trier.de},
      file = F,
      url = {http://wp.me/p5M0LV-3b},
      }
  • Post's Problem for Ordinal Register Machines
    • [DOI] J. D. Hamkins and R. Miller, “Post’s Problem for Ordinal Register Machines,” in Computation and Logic in the Real World–-CiE 2007, Siena, Italy, 2007, pp. 358-367.
      [Bibtex]
      @INPROCEEDINGS{HamkinsMiller2007:PostsProblemForORMs,
      AUTHOR = "Joel David Hamkins and Russell Miller",
      TITLE = "Post's Problem for Ordinal Register Machines",
      BOOKTITLE = "{Computation and Logic in the Real World---CiE 2007}",
      YEAR = "2007",
      editor = "B. Cooper and B. Löwe and A.~Sorbi",
      volume = "4497",
      number = "",
      series = "Proc. LNCS",
      address = "Siena, Italy",
      month = "",
      organization = "",
      publisher = "",
      note = "",
      abstract = "",
      keywords = "",
      pages = {358-367},
      doi = {10.1007/978-3-540-73001-9_37},
      ee = {},
      file = F,
      url = {http://wp.me/p5M0LV-39},
      }
  • The halting problem is decidable on a set of asymptotic probability one
    • [DOI] J. D. Hamkins and A. Miasnikov, “The halting problem is decidable on a set of asymptotic probability one,” Notre Dame Journal of Formal Logic, vol. 47, iss. 4, p. 515–524, 2006.
      [Bibtex]
      @ARTICLE{HamkinsMiasnikov2006:HaltingProblemDecidable,
      AUTHOR = {Hamkins, Joel David and Miasnikov, Alexei},
      TITLE = {The halting problem is decidable on a set of asymptotic probability one},
      JOURNAL = {Notre Dame Journal of Formal Logic},
      VOLUME = {47},
      YEAR = {2006},
      NUMBER = {4},
      PAGES = {515--524},
      ISSN = {0029-4527},
      CODEN = {NDJFAM},
      MRCLASS = {03D10 (68Q05)},
      MRNUMBER = {2272085 (2007m:03082)},
      MRREVIEWER = {Maurice Margenstern},
      DOI = {10.1305/ndjfl/1168352664},
      URL = {http://jdh.hamkins.org/haltingproblemdecidable/},
      eprint = {math/0504351},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      }
  • Diamond (on the regulars) can fail at any strongly unfoldable cardinal
    • [DOI] M. D{u{z}}amonja and J. D. Hamkins, “Diamond (on the regulars) can fail at any strongly unfoldable cardinal,” Ann.~Pure Appl.~Logic, vol. 144, iss. 1-3, p. 83–95, 2006.
      [Bibtex]
      @ARTICLE{DzamonjaHamkins2006:DiamondCanFail,
      AUTHOR = {D{\u{z}}amonja, Mirna and Hamkins, Joel David},
      TITLE = {Diamond (on the regulars) can fail at any strongly unfoldable cardinal},
      JOURNAL = {Ann.~Pure Appl.~Logic},
      FJOURNAL = {Annals of Pure and Applied Logic},
      VOLUME = {144},
      YEAR = {2006},
      NUMBER = {1-3},
      PAGES = {83--95},
      ISSN = {0168-0072},
      CODEN = {APALD7},
      MRCLASS = {03E05 (03E35 03E55)},
      MRNUMBER = {2279655 (2007m:03091)},
      MRREVIEWER = {Andrzej Ros{\l}anowski},
      DOI = {10.1016/j.apal.2006.05.001},
      URL = {http://jdh.hamkins.org/diamondcanfail/},
      month = {December},
      note = {Conference in honor of sixtieth birthday of James E.~Baumgartner},
      eprint = {math/0409304},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      }
  • ${\rm P}\neq{\rm NP}\cap\textrm{co-}{\rm NP}$ for infinite time Turing machines
    • [DOI] V. Deolalikar, J. D. Hamkins, and R. Schindler, “P $\neq$ NP $\cap$ co-NP for infinite time Turing machines,” Journal of Logic and Computation, vol. 15, iss. 5, p. 577–592, 2005.
      [Bibtex]
      @ARTICLE{DeolalikarHamkinsSchindler2005:NPcoNP,
      AUTHOR = {Deolalikar, Vinay and Hamkins, Joel David and Schindler, Ralf},
      TITLE = {P $\neq$ NP $\cap$ co-NP for infinite time {T}uring machines},
      JOURNAL = {Journal of Logic and Computation},
      VOLUME = {15},
      YEAR = {2005},
      NUMBER = {5},
      PAGES = {577--592},
      ISSN = {0955-792X},
      MRCLASS = {68Q05 (03D05 68Q15)},
      MRNUMBER = {2172411 (2006k:68026)},
      MRREVIEWER = {Peter G.~Hinman},
      DOI = {10.1093/logcom/exi022},
      URL = {http://jdh.hamkins.org/np-conp/},
      month = "October",
      eprint = {math/0307388},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      file = F,
      }
  • The necessary maximality principle for c.c.c. forcing is equiconsistent with a weakly compact cardinal
    • [DOI] J. D. Hamkins and W. Woodin, “The necessary maximality principle for c.c.c.~forcing is equiconsistent with a weakly compact cardinal,” Math.~Logic Q., vol. 51, iss. 5, p. 493–498, 2005.
      [Bibtex]
      @ARTICLE{HamkinsWoodin2005:NMPccc,
      AUTHOR = {Joel David Hamkins and W.~Hugh Woodin},
      TITLE = {The necessary maximality principle for c.c.c.~forcing is equiconsistent with a weakly compact cardinal},
      JOURNAL = {Math.~Logic Q.},
      FJOURNAL = {Mathematical Logic Quarterly},
      VOLUME = {51},
      YEAR = {2005},
      NUMBER = {5},
      PAGES = {493--498},
      ISSN = {0942-5616},
      MRCLASS = {03E65 (03E55)},
      MRNUMBER = {2163760 (2006f:03082)},
      MRREVIEWER = {Tetsuya Ishiu},
      DOI = {10.1002/malq.200410045},
      URL = {http://wp.me/s5M0LV-nmpccc},
      eprint = {math/0403165},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      file = F,
      }
  • The Ground Axiom
    • J. D. Hamkins, “The Ground Axiom,” Mathematisches Forschungsinstitut Oberwolfach Report, vol. 55, p. 3160–3162, 2005.
      [Bibtex]
      @ARTICLE{Hamkins2005:TheGroundAxiom,
      AUTHOR = "Joel David Hamkins",
      TITLE = "The {Ground Axiom}",
      JOURNAL = "Mathematisches Forschungsinstitut Oberwolfach Report",
      YEAR = "2005",
      volume = "55",
      number = "",
      pages = "3160--3162",
      month = "",
      note = "",
      abstract = "",
      keywords = "",
      source = "",
      eprint = {1607.00723},
      archivePrefix = {arXiv},
      primaryClass = {math.LO},
      url = {http://jdh.hamkins.org/thegroundaxiom/},
      file = F,
      }
  • Infinitary computability with infinite time Turing machines
    • [DOI] J. D. Hamkins, “Infinitary computability with infinite time Turing machines,” in New Computational Paradigms, 2005.
      [Bibtex]
      @INPROCEEDINGS{Hamkins2005:InfinitaryComputabilityWithITTM,
      AUTHOR = "Joel David Hamkins",
      TITLE = "Infinitary computability with infinite time {Turing} machines",
      BOOKTITLE = "{New Computational Paradigms}",
      YEAR = "2005",
      editor = "B. Cooper and B. Löwe",
      volume = "3526",
      number = "",
      series = "LNCS",
      pages = "",
      address = "",
      month = "June 8-12",
      organization = "CiE",
      publisher = "Springer-Verlag",
      isbn = "3-540-26179-6",
      note = "",
      abstract = "",
      keywords = "",
      doi = {10.1007/11494645_22},
      ee = {},
      file = F,
      url = {http://wp.me/p5M0LV-2H},
      }

3 thoughts on “Publications

  1. Dear Joel David Hamkins,

    I would like to buy your new book “a mathematicians year in japan”. Unfortunately Amazon will not let me buy, most likely because I’m not in the U.S. Is there any way to get a print copy instead of a kindle version? Barring that is there perhaps another way to obtain a copy? Thanks in advance!

    Lee

    • Dear Lee,

      I’m very sorry, but the book is not available in paper format. It currently exists only in electronic format, on Kindle. Kindle format books can be read on almost any device (phone, computer, tablet) with the free Kindle application.

      regards,

      JDH

  2. Pingback: My research collaborators | Joel David Hamkins

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