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

- Google Scholar
- MathSciNet
- Research Gate
- Academia.edu
- PhilPapers
- Math ar$\chi$iv
- DBLP bibliography server

Reviews of my publications are available on

See also

- My mathematical geneology
- My philosophy family tree
- Classificaton and summary of research, Classification of Research 2014

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.)

- 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. (Under review)
`@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 R. Solberg, “Categorical large cardinals and the tension between categoricity and set-theoretic reflection,” Mathematics arXiv, 2020. (Under review)
- Choiceless large cardinals and set-theoretic potentialism
- R. Cutolo and J. D. Hamkins, “Choiceless large cardinals and set-theoretic potentialism,” , p. 10 pages, 2020. (Under review)
`@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 = {}, year = {2020}, volume = {}, number = {}, pages = {10 pages}, month = {}, note = {Under review}, abstract = {}, keywords = {under-review}, source = {}, doi = {}, url = {http://jdh.hamkins.org/choiceless-large-cardinals-and-set-theoretic-potentialism}, eprint = {2007.01690}, archivePrefix = {arXiv}, primaryClass = {math.LO}, }`

- R. Cutolo and J. D. Hamkins, “Choiceless large cardinals and set-theoretic potentialism,” , p. 10 pages, 2020. (Under review)
- Forcing as a computational process
- J. D. Hamkins, R. Miller, and K. J. Williams, “Forcing as a computational process,” Mathematics arXiv, 2020. (Under review)
`@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, R. Miller, and K. J. Williams, “Forcing as a computational process,” Mathematics arXiv, 2020. (Under review)
- My view of Univ
- J. D. Hamkins, My view of Univ, 2020. (The Martlet, Issue 11, Spring 2020, University College, Oxford)
`@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, My view of Univ, 2020. (The Martlet, Issue 11, Spring 2020, University College, Oxford)
- Proof and the Art of Mathematics
- J. D. Hamkins, Proof and the Art of Mathematics, MIT Press, 2020.
`@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, MIT Press, 2020.
- Bi-interpretation in weak set theories
- A. R. Freire and J. D. Hamkins, “Bi-interpretation in weak set theories,” Mathematics arXiv, 2020. (Under review)
`@ARTICLE{FreireHamkins:Bi-interpretation-in-weak-set-theories, author = {Alfredo Roque Freire and Joel David Hamkins}, title = {Bi-interpretation in weak set theories}, journal = {Mathematics arXiv}, year = {2020}, volume = {}, number = {}, pages = {}, month = {}, note = {Under review}, abstract = {}, keywords = {under-review}, source = {}, doi = {}, url = {http://jdh.hamkins.org/bi-interpretation-in-weak-set-theories}, eprint = {2001.05262}, archivePrefix = {arXiv}, primaryClass = {math.LO}, }`

- A. R. Freire and J. D. Hamkins, “Bi-interpretation in weak set theories,” Mathematics arXiv, 2020. (Under review)
- The $\Sigma_1$-definable universal finite sequence
- J. D. Hamkins and K. J. Williams, “The $\Sigma_1$-definable universal finite sequence,” ArXiv e-prints, 2019. (Under review)
`@ARTICLE{HamkinsWilliams:The-universal-finite-sequence, author = {Joel David Hamkins and Kameryn J. Williams}, title = {The $\Sigma_1$-definable universal finite sequence}, journal = {ArXiv e-prints}, year = {2019}, volume = {}, number = {}, pages = {}, month = {}, note = {Under review}, abstract = {}, keywords = {under-review}, eprint = {1909.09100}, archivePrefix = {arXiv}, primaryClass = {math.LO}, source = {}, doi = {}, }`

- J. D. Hamkins and K. J. Williams, “The $\Sigma_1$-definable universal finite sequence,” ArXiv e-prints, 2019. (Under review)
- 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. (Paper~A3, \url{http://math.colgate.edu/~integers/vol20a.html})
`@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}, }`

- D. D. Blair, J. D. Hamkins, and K. O’Bryant, “Representing Ordinal Numbers with Arithmetically Interesting Sets of Real Numbers,” Integers, vol. 20A, 2020. (Paper~A3, \url{http://math.colgate.edu/~integers/vol20a.html})
- Kelley-Morse set theory does not prove the class Fodor principle
- V. Gitman, J. D. Hamkins, and A. Karagila, “Kelley-Morse set theory does not prove the class Fodor theorem,” ArXiv e-prints, 2019. (Manuscript under review)
`@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 = {ArXiv e-prints}, year = {2019}, volume = {}, number = {}, pages = {}, month = {}, note = {Manuscript under review}, abstract = {}, keywords = {under-review}, eprint = {1904.04190}, archivePrefix = {arXiv}, primaryClass = {math.LO}, source = {}, doi = {}, url = {http://wp.me/p5M0LV-1RD}, }`

- V. Gitman, J. D. Hamkins, and A. Karagila, “Kelley-Morse set theory does not prove the class Fodor theorem,” ArXiv e-prints, 2019. (Manuscript under review)
- 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
- M. E. Habič, J. D. Hamkins, L. D. Klausner, J. Verner, and K. J. Williams, “Set-theoretic blockchains,” Archive for Mathematical Logic, 2019.
`@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}, }`

- M. E. Habič, J. D. Hamkins, L. D. Klausner, J. Verner, and K. J. Williams, “Set-theoretic blockchains,” Archive for Mathematical Logic, 2019.
- Topological models of arithmetic
- A. Enayat, J. D. Hamkins, and B. Wcisło, “Topological models of arithmetic,” ArXiv e-prints, 2018. (Under review)
`@ARTICLE{EnayatHamkinsWcislo2018:Topological-models-of-arithmetic, author = {Ali Enayat and Joel David Hamkins and Bartosz Wcisło}, title = {Topological models of arithmetic}, journal = {ArXiv e-prints}, year = {2018}, volume = {}, number = {}, pages = {}, month = {}, note = {Under review}, abstract = {}, keywords = {under-review}, source = {}, doi = {}, eprint = {1808.01270}, archivePrefix = {arXiv}, primaryClass = {math.LO}, url = {http://wp.me/p5M0LV-1LS}, }`

- A. Enayat, J. D. Hamkins, and B. Wcisło, “Topological models of arithmetic,” ArXiv e-prints, 2018. (Under review)
- Open class determinacy is preserved by forcing
- J. D. Hamkins and H. W. Woodin, “Open class determinacy is preserved by forcing,” ArXiv e-prints, pp. 1-14, 2018. (Under review)
`@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 = {ArXiv e-prints}, 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}, }`

- J. D. Hamkins and H. W. Woodin, “Open class determinacy is preserved by forcing,” ArXiv e-prints, pp. 1-14, 2018. (Under review)
- The subseries number
- J. Brendle, W. Brian, and J. D. Hamkins, “The subseries number,” Fund. Math., vol. 247, iss. 1, pp. 49-85, 2019.
`@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. Brendle, W. Brian, and J. D. Hamkins, “The subseries number,” Fund. Math., vol. 247, iss. 1, pp. 49-85, 2019.
- The modal logic of arithmetic potentialism and the universal algorithm
- J. D. Hamkins, “The modal logic of arithmetic potentialism and the universal algorithm,” ArXiv e-prints, pp. 1-35, 2018. (Under review)
`@ARTICLE{Hamkins:The-modal-logic-of-arithmetic-potentialism, author = {Joel David Hamkins}, title = {The modal logic of arithmetic potentialism and the universal algorithm}, journal = {ArXiv e-prints}, 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, “The modal logic of arithmetic potentialism and the universal algorithm,” ArXiv e-prints, pp. 1-35, 2018. (Under review)
- The universal finite set
- J. D. Hamkins and H. W. Woodin, “The universal finite set,” ArXiv e-prints, pp. 1-16, 2017. (Manuscript under review)
`@ARTICLE{HamkinsWoodin:The-universal-finite-set, author = {Joel David Hamkins and W. Hugh Woodin}, title = {The universal finite set}, journal = {ArXiv e-prints}, 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 and H. W. Woodin, “The universal finite set,” ArXiv e-prints, pp. 1-16, 2017. (Manuscript under review)
- 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,” ArXiv e-prints, 2017. (Manuscript under review)
`@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 = {ArXiv e-prints}, 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}, }`

- J. D. Hamkins and J. Reitz, “The set-theoretic universe $V$ is not necessarily a class-forcing extension of HOD,” ArXiv e-prints, 2017. (Manuscript under review)
- Inner-model reflection principles
- N. Barton, A. E. Caicedo, G. Fuchs, J. D. Hamkins, J. Reitz, and R. Schindler, “Inner-model reflection principles,” Studia Logica, vol. 108, pp. 573-595, 2020.
`@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}, }`

- N. Barton, A. E. Caicedo, G. Fuchs, J. D. Hamkins, J. Reitz, and R. Schindler, “Inner-model reflection principles,” Studia Logica, vol. 108, pp. 573-595, 2020.
- The modal logic of set-theoretic potentialism and the potentialist maximality principles
- J. D. Hamkins and Ø. Linnebo, “The modal logic of set-theoretic potentialism and the potentialist maximality principles,” Review of Symbolic Logic, 2019.
`@ARTICLE{HamkinsLinnebo:Modal-logic-of-set-theoretic-potentialism, author = {Hamkins, Joel David and Linnebo, \O{}ystein}, title = {The modal logic of set-theoretic potentialism and the potentialist maximality principles}, journal = {Review of Symbolic Logic}, year = {2019}, volume = {}, number = {}, pages = {}, month = {October}, note = {}, abstract = {}, keywords = {}, source = {}, eprint = {1708.01644}, archivePrefix = {arXiv}, primaryClass = {math.LO}, url = {http://wp.me/p5M0LV-1zC}, doi = {10.1017/S1755020318000242}, }`

- J. D. Hamkins and Ø. Linnebo, “The modal logic of set-theoretic potentialism and the potentialist maximality principles,” Review of Symbolic Logic, 2019.
- 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. (Under review)
`@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}, }`

- G. Fuchs and J. D. Hamkins, “The Bukovský-Dehornoy phenomenon for Boolean ultrapowers,” ArXiv e-prints, 2017. (Under review)
- The exact strength of the class forcing theorem
V. Gitman, J. D. Hamkins, P. Holy, P. Schlicht, and K. Williams, “The exact strength of the class forcing theorem,” Journal of Symbolic Logic, 2020. Citation arχiv @ARTICLE{GitmanHamkinsHolySchlichtWilliams:The-exact-strength-of-the-class-forcing-theorem, author = {Victoria Gitman and Joel David Hamkins and Peter Holy …

- 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.
`@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}, }`

- 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.
- A model of the generic Vopěnka principle in which the ordinals are not $\Delta_2$-Mahlo
- V. Gitman and J. D. Hamkins, “A model of the generic Vopěnka principle in which the ordinals are not Mahlo,” Archive for Mathematical Logic, pp. 1-21, 2018.
`@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.}, }`

- V. Gitman and J. D. Hamkins, “A model of the generic Vopěnka principle in which the ordinals are not Mahlo,” Archive for Mathematical Logic, pp. 1-21, 2018.
- 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. (Manuscript under review)
`@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 = {}, }`

- J. D. Hamkins and M. Kikuchi, “The inclusion relations of the countable models of set theory are all isomorphic,” ArXiv e-prints, 2017. (Manuscript under review)
- Computable quotient presentations of models of arithmetic and set theory
- 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, pp. 140-152.
`@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}, }`

- 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, pp. 140-152.
- The implicitly constructible universe
- M. J. Groszek and J. D. Hamkins, “The implicitly constructible universe,” Journal of Symbolic Logic, vol. 84, iss. 4, pp. 1403-1421, 2019.
`@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}, }`

- M. J. Groszek and J. D. Hamkins, “The implicitly constructible universe,” Journal of Symbolic Logic, vol. 84, iss. 4, pp. 1403-1421, 2019.
- The rearrangement number
- 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, pp. 41-69, 2020.
`@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 = {}, }`

- 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, pp. 41-69, 2020.
- Ord is not definably weakly compact
- 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, pp. 146-164, 2018.
`@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}, }`

- 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, pp. 146-164, 2018.
- 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. (Under review)
`@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}, }`

- J. D. Hamkins, “The Vopěnka principle is inequivalent to but conservative over the Vopěnka scheme,” ArXiv e-prints, 2016. (Under review)
- Set-theoretic mereology
- J. D. Hamkins and M. Kikuchi, “Set-theoretic mereology,” Logic and Logical Philosophy, Special issue “Mereology and beyond, part II”, vol. 25, iss. 3, pp. 285-308, 2016.
`@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 and M. Kikuchi, “Set-theoretic mereology,” Logic and Logical Philosophy, Special issue “Mereology and beyond, part II”, vol. 25, iss. 3, pp. 285-308, 2016.
- 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, pp. 17-31, 2016.
`@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}, }`

- J. D. Hamkins, “Upward closure and amalgamation in the generic multiverse of a countable model of set theory,” RIMS Kyôkyûroku, pp. 17-31, 2016.
- A position in infinite chess with game value $\omega^4$
- 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.
`@ARTICLE{EvansHamkinsPerlmutter: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}, }`

- 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.
- 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)
`@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 = {}, }`

- 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)
- A mathematician’s year in Japan
- J. D. Hamkins, A Mathematician’s Year in Japan, Amazon Kindle Direct Publishing, 2015. (156 pages)
`@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}, }`

- J. D. Hamkins, A Mathematician’s Year in Japan, Amazon Kindle Direct Publishing, 2015. (156 pages)
- Ehrenfeucht’s lemma in set theory
- G. Fuchs, V. Gitman, and J. D. Hamkins, “Ehrenfeucht’s Lemma in Set Theory,” Notre Dame Journal of Formal Logic, vol. 59, iss. 3, pp. 355-370, 2018.
`@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}, }`

- G. Fuchs, V. Gitman, and J. D. Hamkins, “Ehrenfeucht’s Lemma in Set Theory,” Notre Dame Journal of Formal Logic, vol. 59, iss. 3, pp. 355-370, 2018.
- Incomparable $\omega_1$-like models of set theory
- G. Fuchs, V. Gitman, and J. D. Hamkins, “Incomparable $\omega_1$-like models of set theory,” Math.~Logic Q., pp. 1-11, 2017.
`@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}, }`

- G. Fuchs, V. Gitman, and J. D. Hamkins, “Incomparable $\omega_1$-like models of set theory,” Math.~Logic Q., pp. 1-11, 2017.
- Large cardinals need not be large in HOD
- 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.
`@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.", }`

- 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.
- Strongly uplifting cardinals and the boldface resurrection axioms
- J. D. Hamkins and T. Johnstone, “Strongly uplifting cardinals and the boldface resurrection axioms,” Archive for Mathematical Logic, vol. 56, iss. 7, pp. 1115-1133, 2017.
`@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 T. Johnstone, “Strongly uplifting cardinals and the boldface resurrection axioms,” Archive for Mathematical Logic, vol. 56, iss. 7, pp. 1115-1133, 2017.
- Satisfaction is not absolute
- J. D. Hamkins and R. Yang, “Satisfaction is not absolute,” to appear in the Review of Symbolic Logic, pp. 1-34, 2014.
`@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 = {}, }`

- J. D. Hamkins and R. Yang, “Satisfaction is not absolute,” to appear in the Review of Symbolic Logic, pp. 1-34, 2014.
- 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, pp. 89-112.
`@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/}, }`

- 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, pp. 89-112.
- Resurrection axioms and uplifting cardinals
- 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.
`@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, }`

- 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.
- Superstrong and other large cardinals are never Laver indestructible
- 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, pp. 19-35, 2016. (Special volume in memory of R.~Laver)
`@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/}, }`

- 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, pp. 19-35, 2016. (Special volume in memory of R.~Laver)
- The least weakly compact cardinal can be unfoldable, weakly measurable and nearly $\theta$-supercompact
- 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, pp. 1-20, 2015.
`@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}, }`

- 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, pp. 1-20, 2015.
- Algebraicity and implicit definability in set theory
- J. D. Hamkins and C. Leahy, “Algebraicity and Implicit Definability in Set Theory,” Notre Dame Journal of Formal Logic, vol. 57, iss. 3, pp. 431-439, 2016.
`@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}, }`

- J. D. Hamkins and C. Leahy, “Algebraicity and Implicit Definability in Set Theory,” Notre Dame Journal of Formal Logic, vol. 57, iss. 3, pp. 431-439, 2016.
- 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.
`@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 = {}, }`

- C.~D.~A.~Evans and J. D. Hamkins, “Transfinite game values in infinite chess,” Integers, vol. 14, p. Paper No.~G2, 36, 2014.
- A multiverse perspective on the axiom of constructiblity
- J. D. Hamkins, “A multiverse perspective on the axiom of constructibility,” in Infinity and Truth, World Sci. Publ., Hackensack, NJ, 2014, vol. 25, pp. 25-45.
`@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}, }`

- J. D. Hamkins, “A multiverse perspective on the axiom of constructibility,” in Infinity and Truth, World Sci. Publ., Hackensack, NJ, 2014, vol. 25, pp. 25-45.
- 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
- J. D. Hamkins and B. Löwe, “Moving up and down in the generic multiverse,” Logic and its Applications, ICLA 2013 LNCS, vol. 7750, pp. 139-147, 2013.
`@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 = {}, }`

- J. D. Hamkins and B. Löwe, “Moving up and down in the generic multiverse,” Logic and its Applications, ICLA 2013 LNCS, vol. 7750, pp. 139-147, 2013.
- Structural connections between a forcing class and its modal logic
- 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, pp. 617-651, 2015.
`@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}, }`

- 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, pp. 617-651, 2015.
- Every countable model of set theory embeds into its own constructible universe
- 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.
`@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}, }`

- 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.
- Well-founded Boolean ultrapowers as large cardinal embeddings
- J. D. Hamkins and D. Seabold, “Well-founded Boolean ultrapowers as large cardinal embeddings,” , pp. 1-40, 2006.
`@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, }`

- J. D. Hamkins and D. Seabold, “Well-founded Boolean ultrapowers as large cardinal embeddings,” , pp. 1-40, 2006.
- Singular cardinals and strong extenders
- A. W. Apter, J. Cummings, and J. D. Hamkins, “Singular cardinals and strong extenders,” Central European Journal of Mathematics, vol. 11, iss. 9, pp. 1628-1634, 2013.
`@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}, }`

- A. W. Apter, J. Cummings, and J. D. Hamkins, “Singular cardinals and strong extenders,” Central European Journal of Mathematics, vol. 11, iss. 9, pp. 1628-1634, 2013.
- Is the dream solution of the continuum hypothesis attainable?
- J. D. Hamkins, “Is the dream solution of the continuum hypothesis attainable?,” Notre Dame Journal of Formal Logic, vol. 56, iss. 1, pp. 135-145, 2015.
`@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}, }`

- J. D. Hamkins, “Is the dream solution of the continuum hypothesis attainable?,” Notre Dame Journal of Formal Logic, vol. 56, iss. 1, pp. 135-145, 2015.
- The mate-in-n problem of infinite chess is decidable
- 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.
`@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}, }`

- 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.
- Inner models with large cardinal features usually obtained by forcing
- 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, pp. 257-283, 2012.
`@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}, }`

- 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, pp. 257-283, 2012.
- What is the theory ZFC without power set?
- V. Gitman, J. D. Hamkins, and T. A.~Johnstone, “What is the theory ZFC without Powerset?,” Math.~Logic Q., vol. 62, iss. 4–5, pp. 391-406, 2016.
`@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}, }`

- V. Gitman, J. D. Hamkins, and T. A.~Johnstone, “What is the theory ZFC without Powerset?,” Math.~Logic Q., vol. 62, iss. 4–5, pp. 391-406, 2016.
- The hierarchy of equivalence relations on the natural numbers under computable reducibility
- 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, pp. 15-38, 2012.
`@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 = {}, }`

- 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, pp. 15-38, 2012.
- Set-theoretic geology
- G. Fuchs, J. D. Hamkins, and J. Reitz, “Set-theoretic geology,” Annals of Pure and Applied Logic, vol. 166, iss. 4, pp. 464-501, 2015.
`@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", }`

- G. Fuchs, J. D. Hamkins, and J. Reitz, “Set-theoretic geology,” Annals of Pure and Applied Logic, vol. 166, iss. 4, pp. 464-501, 2015.
- The rigid relation principle, a new weak choice principle
- J. D. Hamkins and J. Palumbo, “The rigid relation principle, a new weak choice principle,” Mathematical Logic Quarterly, vol. 58, iss. 6, pp. 394-398, 2012.
`@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/therigidrelationprincipleanewweakacprinciple/}, eprint = {1106.4635}, archivePrefix = {arXiv}, primaryClass = {math.LO}, doi = {10.1002/malq.201100081}, MRNUMBER = {2997028}, MRREVIEWER = {Eleftherios C.~Tachtsis}, abstract = {}, keywords = {}, source = {}, }`

- J. D. Hamkins and J. Palumbo, “The rigid relation principle, a new weak choice principle,” Mathematical Logic Quarterly, vol. 58, iss. 6, pp. 394-398, 2012.
- Generalizations of the Kunen inconsistency
- 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.
`@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", }`

- 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.
- Pointwise definable models of set theory
- J. D. Hamkins, D. Linetsky, and J. Reitz, “Pointwise definable models of set theory,” Journal of Symbolic Logic, vol. 78, iss. 1, pp. 139-156, 2013.
`@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}, }`

- J. D. Hamkins, D. Linetsky, and J. Reitz, “Pointwise definable models of set theory,” Journal of Symbolic Logic, vol. 78, iss. 1, pp. 139-156, 2013.
- 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.
`@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}, url = {http://wp.me/s5M0LV-emu}, source = {}, }`

- 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.
- 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, pp. 33-49.
`@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/}, }`

- 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, pp. 33-49.
- The set-theoretical multiverse
- J. D. Hamkins, “The set-theoretic multiverse,” Review of Symbolic Logic, vol. 5, pp. 416-449, 2012.
`@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}, }`

- J. D. Hamkins, “The set-theoretic multiverse,” Review of Symbolic Logic, vol. 5, pp. 416-449, 2012.
- Infinite time decidable equivalence relation theory
- S. Coskey and J. D. Hamkins, “Infinite time decidable equivalence relation theory,” Notre Dame Journal of Formal Logic, vol. 52, iss. 2, pp. 203-228, 2011.
`@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}, }`

- S. Coskey and J. D. Hamkins, “Infinite time decidable equivalence relation theory,” Notre Dame Journal of Formal Logic, vol. 52, iss. 2, pp. 203-228, 2011.
- The set-theoretical multiverse: a natural context for set theory, Japan 2009
- J. D. Hamkins, “The Set-theoretic Multiverse : A Natural Context for Set Theory,” Annals of the Japan Association for Philosophy of Science, vol. 19, pp. 37-55, 2011.
`@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}, }`

- J. D. Hamkins, “The Set-theoretic Multiverse : A Natural Context for Set Theory,” Annals of the Japan Association for Philosophy of Science, vol. 19, pp. 37-55, 2011.
- A natural model of the multiverse axioms
- V. Gitman and J. D. Hamkins, “A natural model of the multiverse axioms,” Notre Dame Journal of Formal Logic, vol. 51, iss. 4, pp. 475-484, 2010.
`@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}, }`

- V. Gitman and J. D. Hamkins, “A natural model of the multiverse axioms,” Notre Dame Journal of Formal Logic, vol. 51, iss. 4, pp. 475-484, 2010.
- Indestructible strong unfoldability
- J. D. Hamkins and T. A. Johnstone, “Indestructible strong unfoldability,” Notre Dame Journal of Formal Logic, vol. 51, iss. 3, pp. 291-321, 2010.
`@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, }`

- J. D. Hamkins and T. A. Johnstone, “Indestructible strong unfoldability,” Notre Dame Journal of Formal Logic, vol. 51, iss. 3, pp. 291-321, 2010.
- Some second order set theory
- J. D. Hamkins, “Some second order set theory,” in Logic and its Applications, R.~Ramanujam and S.~Sarukkai, Eds., Springer, 2009, vol. 5378, pp. 36-50.
`@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}, }`

- J. D. Hamkins, “Some second order set theory,” in Logic and its Applications, R.~Ramanujam and S.~Sarukkai, Eds., Springer, 2009, vol. 5378, pp. 36-50.
- Post's problem for ordinal register machines: an explicit approach
- 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, pp. 302-309, 2009.
`@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, }`

- 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, pp. 302-309, 2009.
- Degrees of rigidity for Souslin trees
- G. Fuchs and J. D. Hamkins, “Degrees of rigidity for Souslin trees,” Journal of Symbolic Logic, vol. 74, iss. 2, pp. 423-454, 2009.
`@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, }`

- G. Fuchs and J. D. Hamkins, “Degrees of rigidity for Souslin trees,” Journal of Symbolic Logic, vol. 74, iss. 2, pp. 423-454, 2009.
- Tall cardinals
- J. D. Hamkins, “Tall cardinals,” Math.~Logic Q., vol. 55, iss. 1, pp. 68-86, 2009.
`@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, }`

- J. D. Hamkins, “Tall cardinals,” Math.~Logic Q., vol. 55, iss. 1, pp. 68-86, 2009.
- The proper and semi-proper forcing axioms for forcing notions that preserve $\aleph_2$ or $\aleph_3$
- 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, pp. 1823-1833, 2009.
`@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 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, pp. 1823-1833, 2009.
- 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, pp. 521-557.
`@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}, }`

- 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, pp. 521-557.
- Changing the heights of automorphism towers by forcing with Souslin trees over $L$
- 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, pp. 614-633, 2008.
`@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, }`

- 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, pp. 614-633, 2008.
- The ground axiom is consistent with $V\ne{\rm HOD}$
- 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, pp. 2943-2949, 2008.
`@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, }`

- 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, pp. 2943-2949, 2008.
- The modal logic of forcing
- J. D. Hamkins and B. Löwe, “The modal logic of forcing,” Trans.~AMS, vol. 360, iss. 4, pp. 1793-1817, 2008.
`@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}, file = F, }`

- J. D. Hamkins and B. Löwe, “The modal logic of forcing,” Trans.~AMS, vol. 360, iss. 4, pp. 1793-1817, 2008.
- Large cardinals with few measures
- A. W.~Apter, J. Cummings, and J. D. Hamkins, “Large cardinals with few measures,” Proc.~Amer.~Math.~Soc., vol. 135, iss. 7, pp. 2291-2300, 2007.
`@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. W.~Apter, J. Cummings, and J. D. Hamkins, “Large cardinals with few measures,” Proc.~Amer.~Math.~Soc., vol. 135, iss. 7, pp. 2291-2300, 2007.
- A survey of infinite time Turing machines
- J. D. Hamkins, “A Survey of Infinite Time Turing Machines,” in Machines, Computations, and Universality – 5th International Conference MCU 2007, Orleans, France, 2007, pp. 62-71.
`@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}, }`

- J. D. Hamkins, “A Survey of Infinite Time Turing Machines,” in Machines, Computations, and Universality – 5th International Conference MCU 2007, Orleans, France, 2007, pp. 62-71.
- The complexity of quickly decidable ORM-decidable sets
- 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, pp. 488-496.
`@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}, }`

- 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, pp. 488-496.
- Post's Problem for Ordinal Register Machines
- 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.
`@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}, }`

- 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.
- The halting problem is decidable on a set of asymptotic probability one
- 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, pp. 515-524, 2006.
`@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}, file = F, }`

- 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, pp. 515-524, 2006.
- Diamond (on the regulars) can fail at any strongly unfoldable cardinal
- 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, pp. 83-95, 2006. (Conference in honor of sixtieth birthday of James E.~Baumgartner)
`@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}, }`

- 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, pp. 83-95, 2006. (Conference in honor of sixtieth birthday of James E.~Baumgartner)
- ${\rm P}\neq{\rm NP}\cap\textrm{co-}{\rm NP}$ for infinite time Turing machines
- 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, pp. 577-592, 2005.
`@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, }`

- 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, pp. 577-592, 2005.
- The necessary maximality principle for c.c.c. forcing is equiconsistent with a weakly compact cardinal
- 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, pp. 493-498, 2005.
`@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 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, pp. 493-498, 2005.
- The Ground Axiom
- J. D. Hamkins, “The Ground Axiom,” Mathematisches Forschungsinstitut Oberwolfach Report, vol. 55, pp. 3160-3162, 2005.
`@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, }`

- J. D. Hamkins, “The Ground Axiom,” Mathematisches Forschungsinstitut Oberwolfach Report, vol. 55, pp. 3160-3162, 2005.
- Infinitary computability with infinite time Turing machines
- J. D. Hamkins, “Infinitary computability with infinite time Turing machines,” in New Computational Paradigms, 2005.
`@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, “Infinitary computability with infinite time Turing machines,” in New Computational Paradigms, 2005.
- Book review of G. Tourlakis, Lectures in Logic and Set Theory I & II
- 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.
`@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, }`

- 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.
- Supertask computation
- J. D. Hamkins, “Supertask computation,” in Classical and New Paradigms of Computation and their Complexity Hierarchies, Dordrecht, 2004, pp. 141-158. (Papers of the conference “Foundations of the Formal Sciences III” held in Vienna, September 21-24, 2001)
`@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, }`

- J. D. Hamkins, “Supertask computation,” in Classical and New Paradigms of Computation and their Complexity Hierarchies, Dordrecht, 2004, pp. 141-158. (Papers of the conference “Foundations of the Formal Sciences III” held in Vienna, September 21-24, 2001)
- Extensions with the approximation and cover properties have no new large cardinals
- J. D. Hamkins, “Extensions with the approximation and cover properties have no new large cardinals,” Fund.~Math., vol. 180, iss. 3, pp. 257-277, 2003.
`@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, }`

- J. D. Hamkins, “Extensions with the approximation and cover properties have no new large cardinals,” Fund.~Math., vol. 180, iss. 3, pp. 257-277, 2003.
- ${\rm P}^f\neq {\rm NP}^f$ for almost all $f$
- 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, pp. 536-540, 2003.
`@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}, }`

- 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, pp. 536-540, 2003.
- Exactly controlling the non-supercompact strongly compact cardinals
- A. W.~Apter and J. D. Hamkins, “Exactly controlling the non-supercompact strongly compact cardinals,” Journal of Symbolic Logic, vol. 68, iss. 2, pp. 669-688, 2003.
`@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}, }`

- A. W.~Apter and J. D. Hamkins, “Exactly controlling the non-supercompact strongly compact cardinals,” Journal of Symbolic Logic, vol. 68, iss. 2, pp. 669-688, 2003.
- A simple maximality principle
- J. D. Hamkins, “A simple maximality principle,” Journal of Symbolic Logic, vol. 68, iss. 2, pp. 527-550, 2003.
`@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}, }`

- J. D. Hamkins, “A simple maximality principle,” Journal of Symbolic Logic, vol. 68, iss. 2, pp. 527-550, 2003.
- How tall is the automorphism tower of a group?
- 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, pp. 49-57.
`@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}, }`

- 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, pp. 49-57.
- Indestructibility and the level-by-level agreement between strong compactness and supercompactness
- 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, pp. 820-840, 2002.
`@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}, }`

- 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, pp. 820-840, 2002.
- Post's problem for supertasks has both positive and negative solutions
- J. D. Hamkins and A. Lewis, “Post’s problem for supertasks has both positive and negative solutions,” Arch.~Math.~Logic, vol. 41, iss. 6, pp. 507-523, 2002.
`@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 and A. Lewis, “Post’s problem for supertasks has both positive and negative solutions,” Arch.~Math.~Logic, vol. 41, iss. 6, pp. 507-523, 2002.
- Infinite time Turing machines
- J. D. Hamkins, “Infinite time Turing machines,” Minds and Machines, vol. 12, iss. 4, pp. 521-539, 2002. (Special issue devoted to hypercomputation)
`@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}, }`

- J. D. Hamkins, “Infinite time Turing machines,” Minds and Machines, vol. 12, iss. 4, pp. 521-539, 2002. (Special issue devoted to hypercomputation)
- New inconsistencies in infinite utilitarianism
- D. Fishkind, J. D. Hamkins, and B. Montero, “New inconsistencies in infinite utilitarianism,” Australasian Journal of Philosophy, vol. 80, iss. 2, pp. 178-190, 2002.
`@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}, }`

- D. Fishkind, J. D. Hamkins, and B. Montero, “New inconsistencies in infinite utilitarianism,” Australasian Journal of Philosophy, vol. 80, iss. 2, pp. 178-190, 2002.
- Indestructible weakly compact cardinals and the necessity of supercompactness for certain proof schemata
- 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, pp. 563-571, 2001.
`@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}, }`

- 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, pp. 563-571, 2001.
- Unfoldable cardinals and the GCH
- J. D. Hamkins, “Unfoldable cardinals and the GCH,” Journal of Symbolic Logic, vol. 66, iss. 3, pp. 1186-1198, 2001.
`@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}, }`

- J. D. Hamkins, “Unfoldable cardinals and the GCH,” Journal of Symbolic Logic, vol. 66, iss. 3, pp. 1186-1198, 2001.

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

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