# Publications

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

Reviews of my publications are available on

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.)

• 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.” (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 = {},
year = {},
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},
}

• 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},
}

• 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},
}

• 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},
}

• The subseries number
• 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 = {},
}

• 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},
}

• 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},
}

• Inner-model reflection principles
• N. Barton, A. E. Caicedo, G. Fuchs, J. D. Hamkins, and J. Reitz, “Inner-model reflection principles,” ArXiv e-prints, 2017. (manuscript under review)
@ARTICLE{BartonCaicedoFuchsHamkinsReitz:Inner-model-reflection-principles,
author = {Neil Barton and Andr\'es Eduardo Caicedo and Gunter Fuchs and Joel David Hamkins and Jonas Reitz},
title = {Inner-model reflection principles},
journal = {ArXiv e-prints},
year = {2017},
volume = {},
number = {},
pages = {},
month = {},
note = {manuscript under review},
abstract = {},
keywords = {under-review},
source = {},
doi = {},
eprint = {1708.06669},
archivePrefix = {arXiv},
primaryClass = {math.LO},
url = {http://jdh.hamkins.org/inner-model-reflection-principles},
}

• The modal logic of set-theoretic potentialism and the potentialist maximality principles
• J. D. Hamkins and Ø. Linnebo, “The modal logic of set-theoretic potentialism and the potentialist maximality principles,” to appear in Review of Symbolic Logic, 2018.
@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 = {to appear in Review of Symbolic Logic},
year = {2018},
volume = {},
number = {},
pages = {},
month = {},
note = {},
abstract = {},
keywords = {to-appear},
source = {},
eprint = {1708.01644},
archivePrefix = {arXiv},
primaryClass = {math.LO},
url = {http://wp.me/p5M0LV-1zC},
doi = {},
}

• 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},
}

• 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,” ArXiv e-prints, 2017. (manuscript under review)   Citation arχiv @ARTICLE{GitmanHamkinsHolySchlichtWilliams:The-exact-strength-of-the-class-forcing-theorem, author = {Victoria Gitman and Joel David Hamkins and Peter …

• 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?,” to appear in Math Logic Quarterly, 2018.
@ARTICLE{DoraisHamkins:When-does-every-definable-nonempty-set-have-a-definable-element,
author = {Fran\c{c}ois G. Dorais and Joel David Hamkins},
title = {When does every definable nonempty set have a definable element?},
journal = {to appear in Math Logic Quarterly},
year = {2018},
volume = {},
number = {},
pages = {},
month = {},
note = {},
abstract = {},
keywords = {to-appear},
source = {},
doi = {},
eprint = {1706.07285},
archivePrefix = {arXiv},
primaryClass = {math.LO},
url = {http://jdh.hamkins.org/definable-sets-with-definable-elements},
}

• A model of the generic Vopěnka principle in which the ordinals are not $\Delta_2$-Mahlo
• 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.},
}

• 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 = {},
}

• 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",
pages="140--152",
abstract="We prove various extensions of the Tennenbaum phenomenon to the case of computable quotient presentations of models of arithmetic and set theory. Specifically, no nonstandard model of arithmetic has a computable quotient presentation by a c.e. equivalence relation. No {\$}{\$}{\backslash}Sigma {\_}1{\$}{\$} -sound nonstandard model of arithmetic has a computable quotient presentation by a co-c.e. equivalence relation. No nonstandard model of arithmetic in the language {\$}{\$}{\backslash}{\{}+,{\backslash}cdot ,{\backslash}le {\backslash}{\}}{\$}{\$} has a computably enumerable quotient presentation by any equivalence relation of any complexity. No model of ZFC or even much weaker set theories has a computable quotient presentation by any equivalence relation of any complexity. And similarly no nonstandard model of finite set theory has a computable quotient presentation.",
isbn="978-3-662-55386-2",
doi="10.1007/978-3-662-55386-2_10",
eprint = {1702.08350},
archivePrefix = {arXiv},
primaryClass = {math.LO},
url = {http://wp.me/p5M0LV-1tW},
}

• The implicitly constructible universe
• M. J.~Groszek and J. D. Hamkins, “The implicitly constructible universe,” ArXiv e-prints, 2017. (under review)
@ARTICLE{GroszekHamkins:The-implicitly-constructible-universe,
author = {Marcia J.~Groszek and Joel David Hamkins},
title = {The implicitly constructible universe},
journal = {ArXiv e-prints},
year = 2017,
month = feb,
volume = {},
number = {},
pages = {},
month = {},
note = {under review},
abstract = {},
keywords = {under-review},
source = {},
doi = {},
eprint = {1702.07947},
archivePrefix = {arXiv},
primaryClass = {math.LO},
url = {http://jdh.hamkins.org/the-implicitly-constructible-universe},
}

• The rearrangement number
• A. Blass, J. Brendle, W. Brian, J. D. Hamkins, M. Hardy, and P. B. Larson, “The rearrangement number,” ArXiv e-prints, 2016. (manuscript under review)
@ARTICLE{BlassBrendleBrianHamkinsHardyLarson: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 = {ArXiv e-prints},
year = {2016},
volume = {},
number = {},
pages = {},
month = {},
note = {manuscript under review},
url = {http://jdh.hamkins.org/the-rearrangement-number},
eprint = {1612.07830},
archivePrefix = {arXiv},
primaryClass = {math.LO},
abstract = {},
keywords = {under-review},
source = {},
}

• 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,” J.~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 = {J.~Symbolic Logic},
year = {2018},
volume = {83},
number = {1},
pages = {146--164},
month = {},
note = {},
abstract = {},
keywords = {},
source = {},
doi = {10.1017/jsl.2017.75},
eprint = {1610.02729},
archivePrefix = {arXiv},
primaryClass = {math.LO},
url = {http://jdh.hamkins.org/ord-is-not-definably-weakly-compact},
}

• The Vopěnka principle is inequivalent to but conservative over the Vopěnka scheme
• J. D. Hamkins, “The Vopěnka principle is inequivalent to but conservative over the Vopěnka scheme,” ArXiv e-prints, 2016. (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},
}

• 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},
}

• 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},
}

• 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},
}

• 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 = {},
edition = {},
month = {},
note = {Newton Institute preprint ni15064},
url = {http://wp.me/p5M0LV-1af},
eprint = {1509.01099},
archivePrefix = {arXiv},
primaryClass = {math.LO},
abstract = {},
keywords = {},
}

• A mathematician’s year in Japan
• J. D. Hamkins, A Mathematician’s Year in Japan, Amazon Kindle Direct Publishing, 2015. (\href{http://www.amazon.com/dp/B00U618LM2}{ASIN:B00U618LM2}, 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 = {\href{http://www.amazon.com/dp/B00U618LM2}{ASIN:B00U618LM2}, 156 pages},
}

• Ehrenfeucht’s lemma in set theory
• G. Fuchs, V. Gitman, and J. D. Hamkins, “Ehrenfeucht’s Lemma in Set Theory,” Notre Dame J. 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 J. Formal Logic",
number = "3",
pages = "355--370",
publisher = "Duke University Press",
title = "Ehrenfeucht’s Lemma in Set Theory",
volume = "59",
year = "2018",
eprint = {1501.01918},
archivePrefix = {arXiv},
primaryClass = {math.LO},
url = {http://jdh.hamkins.org/ehrenfeuchts-lemma-in-set-theory},
}

• Incomparable $\omega_1$-like models of set theory
• 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},
}

• 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.",
}

• 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 = {},
}

• 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 = {},
}

• 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., Coll. Publ., London, 2014, vol. 23, pp. 89-112.
@incollection {DaghighiGolshaniHaminsJerabek2013:TheFoundationAxiomAndElementarySelfEmbeddingsOfTheUniverse,
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 = {Coll. Publ., London},
EDITOR = {S. Geschke and B. Löwe and P. Schlicht},
YEAR = {2014},
MRCLASS = {03E70 (03E30)},
MRNUMBER = {3307881},
eprint = {1311.0814},
archivePrefix = {arXiv},
primaryClass = {math.LO},
url = {http://jdh.hamkins.org/the-role-of-foundation-in-the-kunen-inconsistency/},
}

• Resurrection axioms and uplifting cardinals
• 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,
}

• 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/},
}

• 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},
}

• Algebraicity and implicit definability in set theory
• J. D. Hamkins and C. Leahy, “Algebraicity and Implicit Definability in Set Theory,” Notre Dame J. 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 J. Formal Logic",
number = "3",
pages = "431--439",
publisher = "Duke University Press",
title = "Algebraicity and Implicit Definability in Set Theory",
volume = "57",
year = "2016",
url = {http://jdh.hamkins.org/algebraicity-and-implicit-definability},
eprint = {1305.5953},
archivePrefix = {arXiv},
primaryClass = {math.LO},
ISSN = {0029-4527},
MRCLASS = {03E47 (03C55)},
MRNUMBER = {3521491},
}

• Transfinite game values in infinite chess
• C.~D.~A.~Evans and J. D. Hamkins, “Transfinite game values in infinite chess,” Integers, vol. 14, p. Paper No.~G2, 36, 2014.
@ARTICLE{EvansHamkins2014:TransfiniteGameValuesInInfiniteChess,
AUTHOR = {C.~D.~A.~Evans and Joel David Hamkins},
TITLE = {Transfinite game values in infinite chess},
JOURNAL = {Integers},
FJOURNAL = {Integers Electronic Journal of Combinatorial Number Theory},
YEAR = {2014},
volume = {14},
number = {},
pages = {Paper No.~G2, 36},
month = {},
note = {},
eprint = {1302.4377},
archivePrefix = {arXiv},
primaryClass = {math.LO},
url = {http://jdh.hamkins.org/game-values-in-infinite-chess},
ISSN = {1553-1732},
MRCLASS = {03Exx (91A46)},
MRNUMBER = {3225916},
abstract = {},
keywords = {},
source = {},
}

• A multiverse perspective on the axiom of constructiblity
• 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},
}

• 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 = {},
}

• 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 J. Math., 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 J. Math.},
FJOURNAL = {Israel Journal of Mathematics},
VOLUME = {207},
YEAR = {2015},
NUMBER = {2},
PAGES = {617--651},
ISSN = {0021-2172},
MRCLASS = {03E40 (03B45)},
MRNUMBER = {3359713},
DOI = {10.1007/s11856-015-1185-5},
url = {http://wp.me/p5M0LV-kf},
eprint = {1207.5841},
archivePrefix = {arXiv},
primaryClass = {math.LO},
}

• Every countable model of set theory embeds into its own constructible universe
• J. D. Hamkins, “Every countable model of set theory embeds into its own constructible universe,” J. Math. 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 = {J. Math. Logic},
FJOURNAL = {J.~Math.~Logic},
VOLUME = {13},
YEAR = {2013},
NUMBER = {2},
PAGES = {1350006, 27},
ISSN = {0219-0613},
MRCLASS = {03C62 (03E99 05C20 05C60 05C63)},
MRNUMBER = {3125902},
MRREVIEWER = {Robert S. Lubarsky},
DOI = {10.1142/S0219061313500062},
eprint = {1207.0963},
archivePrefix = {arXiv},
primaryClass = {math.LO},
URL = {http://wp.me/p5M0LV-jn},
}

• Well-founded Boolean ultrapowers as large cardinal embeddings
• J. D. Hamkins and D. Seabold, “Well-founded Boolean ultrapowers as large cardinal embeddings,” , 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,
}

• Singular cardinals and strong extenders
• A. W. Apter, J. Cummings, and J. D. Hamkins, “Singular cardinals and strong extenders,” Central European J.~Math., 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 J.~Math.},
FJOURNAL = {Central European Journal of Mathematics},
VOLUME = {11},
YEAR = {2013},
NUMBER = {9},
PAGES = {1628--1634},
ISSN = {1895-1074},
MRCLASS = {03E55 (03E35 03E45)},
MRNUMBER = {3071929},
MRREVIEWER = {Samuel Gomes da Silva},
DOI = {10.2478/s11533-013-0265-1},
URL = {http://jdh.hamkins.org/singular-cardinals-strong-extenders/},
eprint = {1206.3703},
archivePrefix = {arXiv},
primaryClass = {math.LO},
}

• Is the dream solution of the continuum hypothesis attainable?
• J. D. Hamkins, “Is the dream solution of the continuum hypothesis attainable?,” Notre Dame J. 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 J. Formal Logic},
FJOURNAL = {Notre Dame Journal of Formal Logic},
VOLUME = {56},
YEAR = {2015},
NUMBER = {1},
PAGES = {135--145},
ISSN = {0029-4527},
MRCLASS = {03E50},
MRNUMBER = {3326592},
MRREVIEWER = {Marek Balcerzak},
DOI = {10.1215/00294527-2835047},
eprint = {1203.4026},
archivePrefix = {arXiv},
primaryClass = {math.LO},
url = {http://jdh.hamkins.org/dream-solution-of-ch},
}

• The mate-in-n problem of infinite chess is decidable
• 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},
}

• 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},
}

• 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},
}

• 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 = {},
}

• 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",
}

• The rigid relation principle, a new weak choice principle
• J. D. Hamkins and J. Palumbo, “The rigid relation principle, a new weak choice principle,” Math.~Logic Q., 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 = {Math.~Logic Q.},
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 = {},
}

• 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",
}

• Pointwise definable models of set theory
• J. D. Hamkins, D. Linetsky, and J. Reitz, “Pointwise definable models of set theory,” J.~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 = {J.~Symbolic Logic},
FJOURNAL = {Journal of Symbolic Logic},
VOLUME = {78},
YEAR = {2013},
NUMBER = {1},
PAGES = {139--156},
ISSN = {0022-4812},
MRCLASS = {03E55},
MRNUMBER = {3087066},
MRREVIEWER = {Bernhard A. König},
DOI = {10.2178/jsl.7801090},
URL = {http://jdh.hamkins.org/pointwisedefinablemodelsofsettheory/},
eprint = "1105.4597",
archivePrefix = {arXiv},
primaryClass = {math.LO},
}

• Effective Mathemematics of the Uncountable
• Effective Mathematics of the Uncountable, N.~Greenberg, J.~D.~Hamkins, D.~R.~Hirschfeldt, and R.~G.~Miller, Eds., Cambridge University Press, ASL Lecture Notes in Logic, 2013, vol. 41.
@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 = {},
edition = {},
month = {},
note = {},
abstract = {},
isbn = {9781107014510},
price = {},
keywords = {book},
url = {http://wp.me/s5M0LV-emu},
source = {},
}

• Infinite time Turing machines and an application to the hierarchy of equivalence relations on the reals
• S. Coskey and J. D. Hamkins, “Infinite time Turing machines and an application to the hierarchy of equivalence relations on the reals,” in Effective mathematics of the uncountable, Assoc. Symbol. Logic, La Jolla, CA, 2013, vol. 41, 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/},
}

• 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},
}

• Infinite time decidable equivalence relation theory
• S. Coskey and J. D. Hamkins, “Infinite time decidable equivalence relation theory,” Notre Dame J.~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 J.~Formal Logic},
FJOURNAL = {Notre Dame Journal of Formal Logic},
VOLUME = {52},
YEAR = {2011},
NUMBER = {2},
PAGES = {203--228},
ISSN = {0029-4527},
MRCLASS = {03D65 (03D30 03E15)},
MRNUMBER = {2794652},
DOI = {10.1215/00294527-1306199},
URL = {http://wp.me/p5M0LV-3M},
eprint = "0910.4616",
archivePrefix = {arXiv},
primaryClass = {math.LO},
}

• The set-theoretical multiverse: a natural context for set theory, Japan 2009
• 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},
}

• A natural model of the multiverse axioms
• V. Gitman and J. D. Hamkins, “A natural model of the multiverse axioms,” Notre Dame J.~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 J.~Formal Logic},
FJOURNAL = {Notre Dame Journal of Formal Logic},
VOLUME = {51},
YEAR = {2010},
NUMBER = {4},
PAGES = {475--484},
ISSN = {0029-4527},
MRCLASS = {03E40},
MRNUMBER = {2741838},
DOI = {10.1215/00294527-2010-030},
URL = {http://wp.me/p5M0LV-3I},
eprint = {1104.4450},
archivePrefix = {arXiv},
primaryClass = {math.LO},
}

• Indestructible strong unfoldability
• J. D. Hamkins and T. A. Johnstone, “Indestructible strong unfoldability,” Notre Dame J.~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 J.~Formal Logic},
FJOURNAL = {Notre Dame Journal of Formal Logic},
VOLUME = {51},
YEAR = {2010},
NUMBER = {3},
PAGES = {291--321},
ISSN = {0029-4527},
MRCLASS = {03E55 (03E40)},
MRNUMBER = {2675684 (2011i:03050)},
MRREVIEWER = {Bernhard A. König},
DOI = {10.1215/00294527-2010-018},
URL = {http://jdh.hamkins.org/indestructiblestrongunfoldability/},
file = F,
}

• Some second order set theory
• 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},
YEAR = {2009},
MRCLASS = {03E35 (03B45 03E40)},
MRNUMBER = {2540935 (2011a:03053)},
DOI = {10.1007/978-3-540-92701-3_3},
URL = {http://wp.me/p5M0LV-3E},
}

• Post's problem for ordinal register machines: an explicit approach
• 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,
}

• Degrees of rigidity for Souslin trees
• G. Fuchs and J. D. Hamkins, “Degrees of rigidity for Souslin trees,” J.~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 = {J.~Symbolic Logic},
FJOURNAL = {Journal of Symbolic Logic},
VOLUME = {74},
YEAR = {2009},
NUMBER = {2},
PAGES = {423--454},
ISSN = {0022-4812},
CODEN = {JSYLA6},
MRCLASS = {03E05},
MRNUMBER = {2518565 (2010i:03049)},
MRREVIEWER = {Stefan Geschke},
URL = {http://wp.me/p5M0LV-3A},
doi = {10.2178/jsl/1243948321},
eprint = {math/0602482},
archivePrefix = {arXiv},
primaryClass = {math.LO},
file = F,
}

• Tall cardinals
• 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,
}

• 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,
}

• 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., New York: 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},
YEAR = {2008},
MRCLASS = {03C57 (03D10)},
MRNUMBER = {2762096},
editor = {S. B. Cooper and Benedikt Löwe and Andrea Sorbi},
isbn = "0-387-36033-6",
file = F,
url = {http://wp.me/p5M0LV-3t},
}

• Changing the heights of automorphism towers by forcing with Souslin trees over $L$
• G. Fuchs and J. D. Hamkins, “Changing the heights of automorphism towers by forcing with Souslin trees over $L$,” J.~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 = {J.~Symbolic Logic},
FJOURNAL = {Journal of Symbolic Logic},
VOLUME = {73},
YEAR = {2008},
NUMBER = {2},
PAGES = {614--633},
ISSN = {0022-4812},
CODEN = {JSYLA6},
MRCLASS = {03E35},
MRNUMBER = {2414468 (2009e:03094)},
MRREVIEWER = {Lutz Struengmann},
URL = {http://wp.me/p5M0LV-3l},
doi = {10.2178/jsl/1208359063},
eprint = {math/0702768},
archivePrefix = {arXiv},
primaryClass = {math.LO},
file = F,
}

• The ground axiom is consistent with $V\ne{\rm HOD}$
• 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,
}

• 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,
}

• 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 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",
month = "",
organization = "",
publisher = "",
note = "",
abstract = "",
keywords = "",
doi = {10.1007/978-3-540-74593-8_5},
file = F,
url = {http://wp.me/p5M0LV-3d},
}

• The complexity of quickly decidable ORM-decidable sets
• 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",
month = "",
organization = "",
publisher = "",
note = "",
abstract = "",
keywords = "",
doi = {10.1007/978-3-540-73001-9_51},
ee = {},
bibsource = {DBLP, http://dblp.uni-trier.de},
file = F,
url = {http://wp.me/p5M0LV-3b},
}

• Post's Problem for Ordinal Register Machines
• 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",
month = "",
organization = "",
publisher = "",
note = "",
abstract = "",
keywords = "",
pages = {358-367},
doi = {10.1007/978-3-540-73001-9_37},
ee = {},
file = F,
url = {http://wp.me/p5M0LV-39},
}

• The halting problem is decidable on a set of asymptotic probability one
• J. D. Hamkins and A. Miasnikov, “The halting problem is decidable on a set of asymptotic probability one,” Notre Dame J.~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 J.~Formal Logic},
FJOURNAL = {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,
}

• 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},
}

• ${\rm P}\neq{\rm NP}\cap\textrm{co-}{\rm NP}$ for infinite time Turing machines
• V. Deolalikar, J. D. Hamkins, and R. Schindler, “P $\neq$ NP $\cap$ co-NP for infinite time Turing machines,” J.~Logic &\ 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 = {J.~Logic \&\ Computation},
FJOURNAL = {Journal of Logic and Computation},
VOLUME = {15},
YEAR = {2005},
NUMBER = {5},
PAGES = {577--592},
ISSN = {0955-792X},
MRCLASS = {68Q05 (03D05 68Q15)},
MRNUMBER = {2172411 (2006k:68026)},
MRREVIEWER = {Peter G.~Hinman},
DOI = {10.1093/logcom/exi022},
URL = {http://jdh.hamkins.org/np-conp/},
month = "October",
eprint = {math/0307388},
archivePrefix = {arXiv},
primaryClass = {math.LO},
file = F,
}

• The necessary maximality principle for c.c.c. forcing is equiconsistent with a weakly compact cardinal
• 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,
}

• 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,
}

• 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",
YEAR = "2005",
editor = "B. Cooper and B. Löwe",
volume = "3526",
number = "",
series = "LNCS",
pages = "",
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},
}

• 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, “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},
BOOKTITLE = {Classical and new paradigms of computation and their complexity hierarchies},
SERIES = {Trends Log.~Stud.~Log.~Libr.},
VOLUME = {23},
PAGES = {141--158},
YEAR = {2004},
MRCLASS = {03D10 (03D25 68Q05)},
MRNUMBER = {2155535},
DOI = {10.1007/978-1-4020-2776-5_8},
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,
}

• 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,
}

• ${\rm P}^f\neq {\rm NP}^f$ 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},
}

• Exactly controlling the non-supercompact strongly compact cardinals
• A. W.~Apter and J. D. Hamkins, “Exactly controlling the non-supercompact strongly compact cardinals,” J.~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 = {J.~Symbolic Logic},
FJOURNAL = {The 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 simple maximality principle
• J. D. Hamkins, “A simple maximality principle,” J.~Symbolic Logic, vol. 68, iss. 2, pp. 527-550, 2003.
@article{Hamkins2003:MaximalityPrinciple,
AUTHOR = {Hamkins, Joel David},
TITLE = {A simple maximality principle},
JOURNAL = {J.~Symbolic Logic},
FJOURNAL = {The 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},
}

• 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},
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},
}

• 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,” J.~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 = {J.~Symbolic Logic},
FJOURNAL = {The 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},
}

• 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},
}

• 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},
}

• New inconsistencies in infinite utilitarianism
• D. Fishkind, J. D. Hamkins, and B. Montero, “New inconsistencies in infinite utilitarianism,” Australasian J.~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 J.~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},
note = {},
}

• 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},
}

• Unfoldable cardinals and the GCH
• J. D. Hamkins, “Unfoldable cardinals and the GCH,” J.~Symbolic Logic, vol. 66, iss. 3, pp. 1186-1198, 2001.
@article{Hamkins2001:UnfoldableCardinals,
AUTHOR = {Hamkins, Joel David},
TITLE = {Unfoldable cardinals and the {GCH}},
JOURNAL = {J.~Symbolic Logic},
FJOURNAL = {The 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},
}

• Gap forcing
• J. D. Hamkins, “Gap forcing,” Israel J.~Math., vol. 125, pp. 237-252, 2001.
@article{Hamkins2001:GapForcing,
AUTHOR = {Hamkins, Joel David},
TITLE = {Gap forcing},
JOURNAL = {Israel J.~Math.},
FJOURNAL = {Israel Journal of Mathematics},
VOLUME = {125},
YEAR = {2001},
PAGES = {237--252},
ISSN = {0021-2172},
CODEN = {ISJMAP},
MRCLASS = {03E40 (03E55)},
MRNUMBER = {1853813 (2002h:03111)},
MRREVIEWER = {Renling Jin},
DOI = {10.1007/BF02773382},
URL = {http://jdh.hamkins.org/gapforcing/},
eprint = {math/9808011},
archivePrefix = {arXiv},
primaryClass = {math.LO},
}

• Infinite time Turing machines with only one tape
• J. D. Hamkins and D. E. Seabold, “Infinite Time Turing Machines With Only One Tape,” Math.~Logic Q., vol. 47, iss. 2, pp. 271-287, 2001.
@article{HamkinsSeabold2001:OneTape,
author = {Hamkins, Joel David and Seabold, Daniel Evan},
title = {Infinite Time {Turing} Machines With Only One Tape},
journal = {Math.~Logic Q.},
volume = {47},
number = {2},
publisher = {WILEY-VCH Verlag Berlin GmbH},
issn = {1521-3870},
MRNUMBER = {1829946 (2002f:03074)},
url = {http://jdh.hamkins.org/onetape/},
doi = {10.1002/1521-3870(200105)47:2<271::AID-MALQ271>3.0.CO;2-6},
pages = {271--287},
keywords = {One-tape infinite Turing machine, Supertask computation},
year = {2001},
eprint = {math/9907044},
archivePrefix = {arXiv},
primaryClass = {math.LO},
}

• The wholeness axioms and $V=\rm HOD$
• J. D. Hamkins, “The wholeness axioms and $V=\rm HOD$,” Arch.~Math.~Logic, vol. 40, iss. 1, pp. 1-8, 2001.
@article{Hamkins2001:WholenessAxiom,
AUTHOR = {Hamkins, Joel David},
TITLE = {The wholeness axioms and {$V=\rm HOD$}},
JOURNAL = {Arch.~Math.~Logic},
FJOURNAL = {Archive for Mathematical Logic},
VOLUME = {40},
YEAR = {2001},
NUMBER = {1},
PAGES = {1--8},
ISSN = {0933-5846},
CODEN = {AMLOEH},
MRCLASS = {03E35 (03E65)},
MRNUMBER = {1816602 (2001m:03102)},
MRREVIEWER = {Ralf-Dieter Schindler},
DOI = {10.1007/s001530050169},
URL = {http://wp.me/p5M0LV-1k},
eprint = {math/9902079},
archivePrefix = {arXiv},
primaryClass = {math.LO},
}

• Infinite time Turing machines
• J. D. Hamkins and A. Lewis, “Infinite time Turing machines,” J.~Symbolic Logic, vol. 65, iss. 2, pp. 567-604, 2000.
@article {HamkinsLewis2000:InfiniteTimeTM,
AUTHOR = {Hamkins, Joel David and Lewis, Andy},
TITLE = {Infinite time {T}uring machines},
JOURNAL = {J.~Symbolic Logic},
FJOURNAL = {The Journal of Symbolic Logic},
VOLUME = {65},
YEAR = {2000},
NUMBER = {2},
PAGES = {567--604},
ISSN = {0022-4812},
CODEN = {JSYLA6},
MRCLASS = {03D10 (03D25 68Q05)},
MRNUMBER = {1771072 (2001g:03072)},
MRREVIEWER = {Robert M.~Baer},
DOI = {10.2307/2586556},
URL = {http://jdh.hamkins.org/ittms/},
eprint = {math/9808093},
archivePrefix = {arXiv},
primaryClass = {math.LO},
}

• The lottery preparation
• J. D. Hamkins, “The lottery preparation,” Ann.~Pure Appl.~Logic, vol. 101, iss. 2-3, pp. 103-146, 2000.
@article {Hamkins2000:LotteryPreparation,
AUTHOR = {Hamkins, Joel David},
TITLE = {The lottery preparation},
JOURNAL = {Ann.~Pure Appl.~Logic},
FJOURNAL = {Annals of Pure and Applied Logic},
VOLUME = {101},
YEAR = {2000},
NUMBER = {2-3},
PAGES = {103--146},
ISSN = {0168-0072},
CODEN = {APALD7},
MRCLASS = {03E55 (03E40)},
MRNUMBER = {1736060 (2001i:03108)},
MRREVIEWER = {Klaas Pieter Hart},
DOI = {10.1016/S0168-0072(99)00010-X},
URL = {http://jdh.hamkins.org/lotterypreparation/},
eprint = {math/9808012},
archivePrefix = {arXiv},
primaryClass = {math.LO},
}

• Changing the heights of automorphism towers
• J. D. Hamkins and S. Thomas, “Changing the heights of automorphism towers,” Ann.~Pure Appl.~Logic, vol. 102, iss. 1-2, pp. 139-157, 2000.
@article {HamkinsThomas2000:ChangingHeights,
AUTHOR = {Hamkins, Joel David and Thomas, Simon},
TITLE = {Changing the heights of automorphism towers},
JOURNAL = {Ann.~Pure Appl.~Logic},
FJOURNAL = {Annals of Pure and Applied Logic},
VOLUME = {102},
YEAR = {2000},
NUMBER = {1-2},
PAGES = {139--157},
ISSN = {0168-0072},
CODEN = {APALD7},
MRCLASS = {20F28 (03E35 20A15)},
MRNUMBER = {1732058 (2000m:20057)},
MRREVIEWER = {Markus Junker},
DOI = {10.1016/S0168-0072(99)00039-1},
URL = {http://jdh.hamkins.org/changingheightsoverl/},
eprint = {math/9703204},
archivePrefix = {arXiv},
primaryClass = {math.LO},
}

• Small forcing creates neither strong nor Woodin cardinals
• J. D. Hamkins and W. Woodin, “Small forcing creates neither strong nor Woodin cardinals,” Proc.~Amer.~Math.~Soc., vol. 128, iss. 10, pp. 3025-3029, 2000.
@article {HamkinsWoodin2000:SmallForcing,
AUTHOR = {Hamkins, Joel David and Woodin, W.~Hugh},
TITLE = {Small forcing creates neither strong nor {W}oodin cardinals},
JOURNAL = {Proc.~Amer.~Math.~Soc.},
FJOURNAL = {Proceedings of the American Mathematical Society},
VOLUME = {128},
YEAR = {2000},
NUMBER = {10},
PAGES = {3025--3029},
ISSN = {0002-9939},
CODEN = {PAMYAR},
MRCLASS = {03E35 (03E55)},
MRNUMBER = {1664390 (2000m:03121)},
MRREVIEWER = {Carlos A.~Di Prisco},
DOI = {10.1090/S0002-9939-00-05347-8},
URL = {http://jdh.hamkins.org/smallforcing-w/},
eprint = {math/9808124},
archivePrefix = {arXiv},
primaryClass = {math.LO},
}

• With infinite utility, more needn’t be better
• J. D. Hamkins and B. Montero, “With infinite utility, more needn’t be better,” Australasian J.~Philosophy, vol. 78, iss. 2, pp. 231-240, 2000.
@article{HamkinsMontero2000:MoreBetter,
author = {Joel David Hamkins and Barbara Montero},
title = {With infinite utility, more needn't be better},
journal = {Australasian J.~Philosophy},
volume = {78},
number = {2},
year = {2000},
pages = {231--240},
url = {http://jdh.hamkins.org/infinite-utility-more-better},
doi = {10.1080/00048400012349511},
}

## 3 thoughts on “Publications”

1. Dear Joel David Hamkins,

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

Lee

• Dear Lee,

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

regards,

JDH