# 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.

• A mathematician’s year in Japan
• J. D. Hamkins, A Mathematician’s Year in Japan, author-published, via Amazon Kindle Direct Publishing, 2015. (ASIN:B00U618LM2, 156 pages, http://www.amazon.com/dp/B00U618LM2)
@BOOK{Hamkins2015:AMathematiciansYearInJapan,
author = {Joel David Hamkins},
title = {A {Mathematician's} {Year} in {Japan}},
publisher = {author-published, via Amazon Kindle Direct Publishing},
year = {2015},
month = {March},
url = {http://www.amazon.com/dp/B00U618LM2},
note = {ASIN:B00U618LM2, 156 pages, http://www.amazon.com/dp/B00U618LM2},
}

• Ehrenfeucht's lemma in set theory
• G. Fuchs, V. Gitman, and J. D. Hamkins, “Ehrenfeucht’s lemma in set theory.” (manuscript under review)
@ARTICLE{FuchsGitmanHamkins:EhrenfeuchtsLemmaInSetTheory,
author = {Gunter Fuchs and Victoria Gitman and Joel David Hamkins},
title = {Ehrenfeucht's lemma in set theory},
journal = {},
year = {},
volume = {},
number = {},
pages = {},
month = {},
eprint = {1501.01918},
note = {manuscript under review},
url = {\url{http://jdh.hamkins.org/ehrenfeuchts-lemma-in-set-theory}},
abstract = {},
keywords = {},
source = {},
}

• Incomparable $\omega_1$-like models of set theory
• G. Fuchs, V. Gitman, and J. D. Hamkins, “Incomparable $\omega_1$-like models of set theory.” (manuscript under review)
@ARTICLE{FuchsGitmanHamkins:IncomparableOmega1-likeModelsOfSetTheory,
author = {Gunter Fuchs and Victoria Gitman and Joel David Hamkins},
title = {Incomparable $\omega_1$-like models of set theory},
journal = {},
year = {},
volume = {},
number = {},
pages = {},
month = {},
eprint = {1501.01022},
note = {manuscript under review},
url = {\url{http://jdh.hamkins.org/incomparable-omega-one-like-models-of-set-theory}},
abstract = {},
keywords = {},
source = {},
}

• Large cardinals need not be large in HOD
• Y. Cheng, S. Friedman, and J. D. Hamkins, “Large cardinals need not be large in HOD.” (manuscript under review)
@ARTICLE{ChengFriedmanHamkins:LargeCardinalsNeedNotBeLargeInHOD,
author = {Yong Cheng and Sy-David Friedman and Joel David Hamkins},
title = {Large cardinals need not be large in {HOD}},
journal = {},
year = {},
volume = {},
number = {},
pages = {},
month = {},
note = {manuscript under review},
eprint = {1407.6335},
url = {\url{http://jdh.hamkins.org/large-cardinals-need-not-be-large-in-hod}},
abstract = {},
keywords = {},
source = {},
}

• Strongly uplifting cardinals and the boldface resurrection axioms
• J. D. Hamkins and T. Johnstone, “Strongly uplifting cardinals and the boldface resurrection axioms.” (under review, http://arxiv.org/abs/1403.2788)
@ARTICLE{HamkinsJohnstone:StronglyUpliftingCardinalsAndBoldfaceResurrection,
author = {Joel David Hamkins and Thomas Johnstone},
title = {Strongly uplifting cardinals and the boldface resurrection axioms},
journal = {},
year = {},
volume = {},
number = {},
pages = {},
month = {},
note = {under review, http://arxiv.org/abs/1403.2788},
eprint = {1403.2788},
url = {http://jdh.hamkins.org/strongly-uplifting-cardinals-and-boldface-resurrection},
abstract = {},
keywords = {},
source = {},
}

• Satisfaction is not absolute
• J. D. Hamkins and R. Yang, “Satisfaction is not absolute,” , pp. 1-34. (under review)
@ARTICLE{HamkinsYang:SatisfactionIsNotAbsolute,
author = {Joel David Hamkins and Ruizhi Yang},
title = {Satisfaction is not absolute},
journal = {},
year = {},
volume = {},
number = {},
pages = {1--34},
month = {},
note = {under review},
abstract = {},
keywords = {},
source = {},
eprint = {1312.0670},
url = {http://jdh.hamkins.org/satisfaction-is-not-absolute},
doi = {},
}

• The foundation axiom and elementary self-embeddings of the universe
• A. S. Daghighi, M. Golshani, J. D. Hamkins, and E. Jev rábek, “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, London, 2014, p. p. 89–112.
@INPROCEEDINGS{DaghighiGolshaniHaminsJerabek2013:TheFoundationAxiomAndElementarySelfEmbeddingsOfTheUniverse,
author = {Ali Sadegh Daghighi and Mohammad Golshani and Joel David Hamkins and Emil {Je\v r\'abek}},
booktitle = {Infinity, computability, and metamathematics:
Festschrift celebrating the 60th birthdays of Peter Koepke
and Philip Welch},
title = {The foundation axiom and elementary self-embeddings of the universe},
YEAR = {2014},
SERIES = {Tributes},
VOLUME = {23},
EDITOR = {Geschke, Stefan and L\"owe, Benedikt and Schlicht, Philipp},
number = {},
pages = {p. 89--112},
month = {},
organization = {},
PUBLISHER = {College Publications},
eprint = {1311.0814},
url = {http://jdh.hamkins.org/the-role-of-foundation-in-the-kunen-inconsistency/},
note = {},
abstract = {},
keywords = {},
}

• 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",
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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,” to appear in Archive for Mathematical Logic (special issue in honor of Richard Laver).
@ARTICLE{BagariaHamkinsTsaprounisUsuba:SuperstrongAndOtherLargeCardinalsAreNeverLaverIndestructible,
author = {Joan Bagaria and Joel David Hamkins and Konstantinos Tsaprounis and Toshimichi Usuba},
title = {Superstrong and other large cardinals are never {Laver} indestructible},
journal = {to appear in Archive for Mathematical Logic (special issue in honor of Richard Laver)},
year = {},
volume = {},
number = {},
pages = {},
month = {},
note = {},
abstract = {},
keywords = {},
eprint = {1307.3486},
url = {http://jdh.hamkins.org/superstrong-never-indestructible/},
comment = {http://jdh.hamkins.org/superstrong-never-indestructible/},
source = {},
}

• The least weakly compact cardinal can be unfoldable, weakly measurable and nearly $\theta$-supercompact
• B. Cody, M. Gitik, J. D. Hamkins, and J. Schanker, “The least weakly compact cardinal can be unfoldable, weakly measurable and nearly $\theta$-supercompact,” to appear in the Annals of Pure and Applied Logic, pp. 1-24.
@ARTICLE{CodyGitikHamkinsSchanker:LeastWeaklyCompact,
author = {Brent Cody and Moti Gitik and Joel David Hamkins and Jason Schanker},
title = {The least weakly compact cardinal can be unfoldable, weakly measurable and nearly $\theta$-supercompact},
journal = {to appear in the Annals of Pure and Applied Logic},
year = {},
volume = {},
number = {},
pages = {1--24},
month = {},
note = {},
eprint = {1305.5961},
abstract = {},
keywords = {},
source = {},
}

• Algebraicity and implicit definability in set theory
• J. D. Hamkins and C. Leahy, “Algebraicity and implicit definability in set theory,” to appear in Notre Dame Journal of Formal Logic.
@ARTICLE{HamkinsLeahy:AlgebraicityAndImplicitDefinabilityInSetTheory,
author = {Joel David Hamkins and Cole Leahy},
title = {Algebraicity and implicit definability in set theory},
journal = {to appear in {N}otre {D}ame {J}ournal of {F}ormal {L}ogic},
year = {},
volume = {},
number = {},
pages = {},
month = {},
note = {},
url = {http://jdh.hamkins.org/algebraicity-and-implicit-definability},
eprint = {1305.5953},
abstract = {},
keywords = {},
source = {},
}

• 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},
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.” , 2013, vol. 25.
@INBOOK{Hamkins2013:MultiverseOnVeqL,
author = {Joel David Hamkins},
editor = {},
title = {A multiverse perspective on the axiom of constructibility, in Infinity and Truth},
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year = {2013},
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series = {IMS Lecture Note Series, NUS},
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month = {},
note = {},
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url = {http://arxiv.org/abs/1210.6541},
eprint = {1210.6541},
doi = {},
}

• 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 L\"owe},
title = {Moving up and down in the generic multiverse},
journal = {Logic and its Applications, ICLA 2013 LNCS},
publisher={Springer Berlin Heidelberg},
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://jdh.hamkins.org/up-and-down-in-the-generic-multiverse},
url = {http://arxiv.org/abs/1208.5061},
eprint = {1208.5061},
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,” to appear in the Israel Journal of Mathematics, pp. 1-23.
@ARTICLE{HamkinsLeibmanLoewe:StructuralConnectionsForcingClassAndItsModalLogic,
AUTHOR = {Joel David Hamkins and George Leibman and Benedikt L\"owe},
TITLE = {Structural connections between a forcing class and its modal logic},
JOURNAL = {to appear in the Israel Journal of Mathematics},
YEAR = {},
volume = {},
number = {},
pages = {1--23},
month = {},
note = {},
url = {http://arxiv.org/abs/1207.5841},
url = {http://jdh.hamkins.org/a-forcing-class-and-its-modal-logic},
eprint = {1207.5841},
abstract = {},
keywords = {},
source = {},
}

• 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, 2013.
@ARTICLE{Hamkins2013:EveryCountableModelOfSetTheoryEmbedsIntoItsOwnL,
author = {Joel David Hamkins},
title = {Every countable model of set theory embeds into its own constructible universe},
journal = {Journal of Mathematical Logic},
year = {2013},
volume = {13},
number = {2},
pages = {1350006},
month = {},
note = {},
abstract = {},
keywords = {},
source = {},
doi = {10.1142/S0219061313500062},
eprint = {1207.0963},
URL = {http://jdh.hamkins.org/every-model-embeds-into-own-constructible-universe/},
}

• 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. (preprint \url{http://jdh.hamkins.org/boolean-ultrapowers/})
@ARTICLE{HamkinsSeabold:BooleanUltrapowers,
AUTHOR = "Joel David Hamkins and Daniel Seabold",
TITLE = "Well-founded {Boolean} ultrapowers as large cardinal embeddings",
JOURNAL = "",
YEAR = "",
volume = "",
number = "",
pages = "1--40",
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note = "preprint \url{http://jdh.hamkins.org/boolean-ultrapowers/}",
eprint = "1206.6075",
url = {http://arxiv.org/abs/1206.6075},
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 Journal of Mathematics, vol. 11, iss. 9, pp. 1628-1634, 2013.
@ARTICLE{ApterCummingsHamkins2013:SingularCardinalsAndStrongExtenders,
author = {Arthur W. Apter and James Cummings and Joel David Hamkins},
title = {Singular cardinals and strong extenders},
journal = {Central European Journal of Mathematics},
year = {2013},
volume = {11},
number = {9},
pages = {1628--1634},
month = {},
url = {http://arxiv.org/abs/1206.3703},
eprint = {1206.3703},
doi = {10.2478/s11533-013-0265-1},
note = {},
abstract = {},
keywords = {},
source = {},
}

• 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 (to appear), pp. 1-10.
@ARTICLE{Hamkins:IsTheDreamSolutionToTheContinuumHypothesisAttainable,
AUTHOR = {Joel David Hamkins},
TITLE = {Is the dream solution of the continuum hypothesis attainable?},
JOURNAL = {Notre Dame Journal of Formal Logic (to appear)},
YEAR = {},
volume = {},
number = {},
pages = {1--10},
month = {},
note = {},
abstract = {},
keywords = {},
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eprint = {1203.4026},
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 Berlin Heidelberg, 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://dx.doi.org/10.1007/978-3-642-30870-3_9},
publisher={Springer Berlin Heidelberg},
author={Brumleve, Dan and Hamkins, Joel David and Schlicht, Philipp},
pages={78-88},
eprint = {1201.5597},
}

• Inner models with large cardinal features usually obtained by forcing
• A. Apter, V. Gitman, and J. D. Hamkins, “Inner models with large cardinal features usually obtained by forcing,” Archive for Mathematical Logic, vol. 51, pp. 257-283, 2012. (10.1007/s00153-011-0264-5)
@article {ApterGitmanHamkins2012:InnerModelsWithLargeCardinals,
author = {Apter, Arthur and Gitman, Victoria and Hamkins, Joel David},
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 Mathematical Logic},
publisher = {Springer Berlin / Heidelberg},
issn = {0933-5846},
keyword = {Mathematics and Statistics},
pages = {257--283},
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eprint = {1111.0856},
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note = {10.1007/s00153-011-0264-5},
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?.” (under review)
@ARTICLE{GitmanHamkinsJohnstone:WhatIsTheTheoryZFC-Powerset?,
AUTHOR = {Victoria Gitman and Joel David Hamkins and Thomas A. Johnstone},
TITLE = {What is the theory {ZFC} without {Powerset}?},
JOURNAL = {},
YEAR = {},
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eprint = {1110.2430},
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}

• 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://iospress.metapress.com/content/96X98U84V504G456},
eprint = {1109.3375},
doi = {10.3233/COM-2012-004},
abstract = {},
keywords = {},
source = {},
}

• Set-theoretic geology
• 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},
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},
url = "http://www.sciencedirect.com/science/article/pii/S0168007212000966",
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,” Journal of Symbolic Logic, vol. 78, iss. 1, pp. 139-156, 2013.
@ARTICLE{HamkinsLinetskyReitz2013:PointwiseDefinableModelsOfSetTheory,
AUTHOR = "Joel David Hamkins and David Linetsky and Jonas Reitz",
TITLE = "Pointwise definable models of set theory",
JOURNAL = "Journal of Symbolic Logic",
YEAR = "2013",
volume = "78",
number = "1",
pages = "139--156",
month = "",
note = "",
url = "http://projecteuclid.org/euclid.jsl/1358951104",
abstract = "",
keywords = "",
source = "",
eprint = "1105.4597",
doi = "10.2178/jsl.7801090",
file = F
}

• 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},
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YEAR = {2013},
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• 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,” Book chapter, ASL Lecture Notes in Logic NL volume Effective Mathematics of the Uncountable, vol. 41, 2013.
@ARTICLE{CoskeyHamkins2013:ITTMandApplicationsToEquivRelations,
AUTHOR = {Samuel Coskey and Joel David Hamkins},
TITLE = {Infinite time {Turing} machines and an application to the hierarchy of equivalence relations on the reals},
JOURNAL = {Book chapter, {ASL} {L}ecture {N}otes in {L}ogic {NL} volume Effective Mathematics of the Uncountable},
YEAR = {2013},
volume = {41},
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month = {},
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abstract = {},
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source = {},
eprint = {1101.1864},
url = {http://arxiv.org/abs/1101.1864},
}

• 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 = {},
doi = {10.1017/S1755020311000359},
abstract = {},
keywords = {},
source = {},
eprint = {1108.4223},
url = {http://jdh.hamkins.org/themultiverse},
}

• Infinite time decidable equivalence relation theory
• S. Coskey and J. D. Hamkins, “Infinite time decidable equivalence relation theory,” Notre Dame J. Form. Log., 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. Form. Log.},
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://dx.doi.org/10.1215/00294527-1306199},
eprint = "0910.4616",
file = F
}

• 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://ci.nii.ac.jp/naid/110008722567/en/",
DOI="",
}

• A natural model of the multiverse axioms
• V. Gitman and J. D. Hamkins, “A natural model of the multiverse axioms,” Notre Dame J. Form. Log., vol. 51, iss. 4, pp. 475-484, 2010.
@ARTICLE{GitmanHamkins2010:NaturalModelOfMultiverseAxioms,
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• Indestructible strong unfoldability
• J. D. Hamkins and T. A. Johnstone, “Indestructible strong unfoldability,” Notre Dame J. Form. Log., vol. 51, iss. 3, pp. 291-321, 2010.
@ARTICLE{HamkinsJohnstone2010:IndestructibleStrongUnfoldability,
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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., Berlin: Springer, 2009, vol. 5378, pp. 36-50.
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AUTHOR = {Hamkins, Joel David},
TITLE = {Some second order set theory},
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PAGES = {36--50},
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}

• 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,
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TITLE = {Post's problem for ordinal register machines: an explicit approach},
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FJOURNAL = {Annals of Pure and Applied Logic},
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DOI = {10.1016/j.apal.2009.01.004},
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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},
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MRREVIEWER = {Stefan Geschke},
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doi = {10.2178/jsl/1243948321},
eprint = {math/0602482},
file = F
}

• Tall cardinals
• J. D. Hamkins, “Tall cardinals,” MLQ Math. Log. Q., vol. 55, iss. 1, pp. 68-86, 2009.
@ARTICLE{Hamkins2009:TallCardinals,
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TITLE = {Tall cardinals},
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NUMBER = {1},
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MRNUMBER = {2489293 (2010g:03083)},
MRREVIEWER = {Carlos A. Di Prisco},
DOI = {10.1002/malq.200710084},
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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.},
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NUMBER = {5},
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MRNUMBER = {2470843 (2009k:03087)},
MRREVIEWER = {John Krueger},
DOI = {10.1090/S0002-9939-08-09727-X},
URL = {http://dx.doi.org/10.1090/S0002-9939-08-09727-X},
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,
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and Warner, Steve},
TITLE = {Infinite time computable model theory},
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PAGES = {521--557},
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MRCLASS = {03C57 (03D10)},
MRNUMBER = {2762096},
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file = F
}

• 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},
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ISSN = {0022-4812},
CODEN = {JSYLA6},
MRCLASS = {03E35},
MRNUMBER = {2414468 (2009e:03094)},
MRREVIEWER = {Lutz Struengmann},
URL = {http://dx.doi.org/10.2178/jsl/1208359063},
doi = {10.2178/jsl/1208359063},
eprint = {math/0702768},
file = F
}

• The ground axiom is consistent with $V\ne{\rm HOD}$
• J. D. Hamkins, J. Reitz, and H. 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},
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MRNUMBER = {2399062 (2009b:03137)},
MRREVIEWER = {P{\'e}ter Komj{\'a}th},
DOI = {10.1090/S0002-9939-08-09285-X},
URL = {http://dx.doi.org/10.1090/S0002-9939-08-09285-X},
file = F
}

• The modal logic of forcing
• J. D. Hamkins and B. Löwe, “The modal logic of forcing,” Trans. Amer. Math. Soc., vol. 360, iss. 4, pp. 1793-1817, 2008.
@ARTICLE{HamkinsLoewe2008:TheModalLogicOfForcing,
AUTHOR = {Hamkins, Joel David and L{\"o}we, Benedikt},
TITLE = {The modal logic of forcing},
JOURNAL = {Trans. Amer. Math. Soc.},
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://dx.doi.org/10.1090/S0002-9947-07-04297-3},
eprint = {math/0509616},
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 = {Apter, Arthur W. and Cummings, James and Hamkins, Joel David},
TITLE = {Large cardinals with few measures},
JOURNAL = {Proc. Amer. Math. Soc.},
FJOURNAL = {Proceedings of the American Mathematical Society},
VOLUME = {135},
YEAR = {2007},
NUMBER = {7},
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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://dx.doi.org/10.1090/S0002-9939-07-08786-2},
eprint = {math/0603260},
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,
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file = F
}

• 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 – Third Conference of Computability in Europe CiE 2007, Siena, Italy, 2007, pp. 488-496.
@INPROCEEDINGS{HamkinsLinetskyMiller2007:ComplexityOfQuicklyDecidableORMSets,
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bibsource = {DBLP, http://dblp.uni-trier.de},
file = F
}

• 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—Third Conference of Computability in Europe CiE 2007, Siena, Italy, 2007, pp. 358-367.
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file = F
}

• 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},
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MRCLASS = {03D10 (68Q05)},
MRNUMBER = {2272085 (2007m:03082)},
MRREVIEWER = {Maurice Margenstern},
DOI = {10.1305/ndjfl/1168352664},
URL = {http://dx.doi.org/10.1305/ndjfl/1168352664},
eprint = {math/0504351},
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://dx.doi.org/10.1016/j.apal.2006.05.001},
month = {December},
note = {Conference in honor of sixtieth birthday of James E. Baumgartner},
eprint = {math/0409304},
}

• ${\rm P}\neq{\rm NP}\cap\textrm{co-}{\rm NP}$ for infinite time Turing machines
• V. Deolalikar, J. D. Hamkins, and R. Schindler, “${\rm P}\neq{\rm NP}\cap$ co-NP for infinite time Turing machines,” J. Logic Comput., vol. 15, iss. 5, pp. 577-592, 2005.
@ARTICLE{DeolalikarHamkinsSchindler2005:NPcoNP,
AUTHOR = {Deolalikar, Vinay and Hamkins, Joel David and Schindler, Ralf},
TITLE = {{${\rm P}\neq{\rm NP}\cap$} co-{NP} for infinite time {T}uring machines},
JOURNAL = {J. Logic Comput.},
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://dx.doi.org/10.1093/logcom/exi022},
month = "October",
eprint = {math/0307388},
file = F,
}

• The necessary maximality principle for c.c.c. forcing is equiconsistent with a weakly compact cardinal
• J. D. Hamkins and H. W. Woodin, “The necessary maximality principle for c.c.c.\ forcing is equiconsistent with a weakly compact cardinal,” MLQ Math. Log. Q., vol. 51, iss. 5, pp. 493-498, 2005.
@ARTICLE{HamkinsWoodin2005:NMPccc,
AUTHOR = {Hamkins, Joel D. and Woodin, W. Hugh},
TITLE = {The necessary maximality principle for c.c.c.\ forcing is equiconsistent with a weakly compact cardinal},
JOURNAL = {MLQ Math. Log. Q.},
FJOURNAL = {MLQ. 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://dx.doi.org/10.1002/malq.200410045},
eprint = {math/0403165},
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 = "",
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• Infinitary computability with infinite time Turing machines
• J. D. Hamkins, “Infinitary computability with infinite time Turing machines,” in New Computational Paradigms, Amsterdam, 2005.
@INPROCEEDINGS{Hamkins2005:InfinitaryComputabilityWithITTM,
AUTHOR = "Joel David Hamkins",
TITLE = "Infinitary computability with infinite time {T}uring machines",
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}

• 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 = "",
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keywords = "",
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• 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},
URL = {http://dx.doi.org/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},
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://dx.doi.org/10.4064/fm180-3-4},
eprint = {math/0307229},
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 $f$,” MLQ Math. Log. 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 = {MLQ Math. Log. Q.},
FJOURNAL = {MLQ. 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://dx.doi.org/10.1002/malq.200310057},
eprint = {math/0212046},
}

• 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 = {Apter, Arthur W. and Hamkins, Joel David},
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},
URL = {http://projecteuclid.org/getRecord?id=euclid.jsl/1052669070},
eprint = {math/0301016},
}

• 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://projecteuclid.org/getRecord?id=euclid.jsl/1052669062},
month = {June},
eprint = {math/0009240},
}

• 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: Amer. Math. Soc., 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 = {Contemp. Math.},
VOLUME = {302},
PAGES = {49--57},
PUBLISHER = {Amer. Math. Soc.},
YEAR = {2002},
MRCLASS = {20E36 (03E35 20A15 20F28)},
MRNUMBER = {1928383 (2003g:20048)},
MRREVIEWER = {Martyn R. Dixon},
editor = {Yi Zhang},
}

• 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 = {Apter, Arthur W. and Hamkins, Joel David},
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://dx.doi.org/10.2178/jsl/1190150111},
eprint = {math/0102086},
}

• 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://dx.doi.org/10.1007/s001530100112},
eprint = {math/9808128},
}

• 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},
}

• 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://dx.doi.org/10.1093/ajp/80.2.178},
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,” MLQ Math. Log. Q., vol. 47, iss. 4, pp. 563-571, 2001.
@ARTICLE{ApterHamkins2001:IndestructibleWC,
AUTHOR = {Apter, Arthur W. and Hamkins, Joel David},
TITLE = {Indestructible weakly compact cardinals and the necessity of supercompactness for certain proof schemata},
JOURNAL = {MLQ Math. Log. Q.},
FJOURNAL = {MLQ. 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://dx.doi.org/10.1002/1521-3870(200111)47:4<563::AID-MALQ563>3.0.CO;2-#},
eprint = {math/9907046}
}

• 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://dx.doi.org/10.2307/2695100},
eprint = {math/9909029}
}

• 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://dx.doi.org/10.1007/BF02773382},
eprint = {math/9808011}
}

• Infinite time Turing machines with only one tape
• J. D. Hamkins and D. E. Seabold, “Infinite Time Turing Machines With Only One Tape,” Mathematical Logic Quarterly, 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 = {Mathematical Logic Quarterly},
volume = {47},
number = {2},
publisher = {WILEY-VCH Verlag Berlin GmbH},
issn = {1521-3870},
MRNUMBER = {1829946 (2002f:03074)},
url = {http://dx.doi.org/10.1002/1521-3870(200105)47:2<271::AID-MALQ271>3.0.CO;2-6},
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},
}

• 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://dx.doi.org/10.1007/s001530050169},
eprint = {math/9902079}
}

• 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://dx.doi.org/10.2307/2586556},
eprint = {math/9808093}
}

• 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://dx.doi.org/10.1016/S0168-0072(99)00010-X},
eprint = {math/9808012}
}

• 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://dx.doi.org/10.1016/S0168-0072(99)00039-1},
eprint = {math/9703204}
}

• Small forcing creates neither strong nor Woodin cardinals
• J. D. Hamkins and H. 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://dx.doi.org/10.1090/S0002-9939-00-05347-8},
eprint = {math/9808124}
}

• With infinite utility, more needn't be better
• J. D. Hamkins and B. Montero, “With infinite utility, more needn’t be better,” Australasian Journal of 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 Journal of Philosophy},
volume = {78},
number = {2},
year = {2000},
pages = {231--240},
url = {http://dx.doi.org/10.1080/00048400012349511},
doi = {10.1080/00048400012349511},
}

• Utilitarianism in infinite worlds
• J. D. Hamkins and B. Montero, “Utilitarianism in infinite worlds,” Utilitas, vol. 12, iss. 1, pp. 91-96, 2000.
@article{HamkinsMontero2000:InfiniteWorlds,
author = {Joel David Hamkins and Barbara Montero},
title = {Utilitarianism in infinite worlds},
journal = {Utilitas},
volume = {12},
number = {1},
year = {2000},
pages = {91--96},
url = {http://dx.doi.org/10.1017/S0953820800002648},
doi = {10.1017/S0953820800002648},
}

• Book review of The Higher Infinite, Akihiro Kanamori
• J. D. Hamkins, “book review of The Higher Infinite, Akihiro Kanamori,” Studia Logica, vol. 65, iss. 3, pp. 443-446, 2000.
@ARTICLE{Hamkins2000:BookReviewKanamori,
AUTHOR = "Joel David Hamkins",
TITLE = "book review of {The Higher Infinite, Akihiro Kanamori}",
JOURNAL = "Studia Logica",
publisher = "Springer Netherlands",
YEAR = "2000",
volume = "65",
number = "3",
pages = "443--446",
month = "",
note = "",
abstract = "",
doi = "10.1023/A:1017327516639",
url = "http://dx.doi.org/10.1023/A:1017327516639",
issn = "0039-3215",
keywords = "",
source = "",
file = F
}

• Gap forcing: generalizing the Lévy-Solovay theorem
• J. D. Hamkins, “Gap forcing: generalizing the Lévy-Solovay theorem,” Bull. Symbolic Logic, vol. 5, iss. 2, pp. 264-272, 1999.
@article{Hamkins99:GapForcingGen,
AUTHOR = {Hamkins, Joel David},
TITLE = {Gap forcing: generalizing the {L}\'evy-{S}olovay theorem},
JOURNAL = {Bull. Symbolic Logic},
FJOURNAL = {The Bulletin of Symbolic Logic},
VOLUME = {5},
YEAR = {1999},
NUMBER = {2},
PAGES = {264--272},
ISSN = {1079-8986},
MRCLASS = {03E40 (03E55)},
MRNUMBER = {1792281 (2002g:03106)},
MRREVIEWER = {Carlos A. Di Prisco},
DOI = {10.2307/421092},
URL = {http://dx.doi.org/10.2307/421092},
month = {June},
eprint = {math/9901108}
}

• Universal indestructibility
• A. W. Apter and J. D. Hamkins, “Universal indestructibility,” Kobe J. Math., vol. 16, iss. 2, pp. 119-130, 1999.
@article {ApterHamkins99:UniversalIndestructibility,
AUTHOR = {Apter, Arthur W. and Hamkins, Joel David},
TITLE = {Universal indestructibility},
JOURNAL = {Kobe J. Math.},
FJOURNAL = {Kobe Journal of Mathematics},
VOLUME = {16},
YEAR = {1999},
NUMBER = {2},
PAGES = {119--130},
ISSN = {0289-9051},
MRCLASS = {03E55 (03E35)},
MRNUMBER = {1745027 (2001k:03112)},
MRNUMBER = {1 745 027},
eprint = {math/9808004}
}

• Superdestructibility: a dual to Laver's indestructibility
• J. D. Hamkins and S. Shelah, “Superdestructibility: a dual to Laver’s indestructibility,” J. Symbolic Logic, vol. 63, iss. 2, pp. 549-554, 1998. ([HmSh:618])
@article {HamkinsShelah98:Dual,
AUTHOR = {Hamkins, Joel David and Shelah, Saharon},
TITLE = {Superdestructibility: a dual to {L}aver's indestructibility},
JOURNAL = {J. Symbolic Logic},
FJOURNAL = {The Journal of Symbolic Logic},
VOLUME = {63},
YEAR = {1998},
NUMBER = {2},
PAGES = {549--554},
ISSN = {0022-4812},
CODEN = {JSYLA6},
MRCLASS = {03E55 (03E40)},
MRNUMBER = {1625927 (99m:03106)},
MRREVIEWER = {Douglas R. Burke},
DOI = {10.2307/2586848},
URL = {http://dx.doi.org/10.2307/2586848},
note = {[HmSh:618]},
eprint = {math/9612227}
}

• Small forcing makes any cardinal superdestructible
• J. D. Hamkins, “Small forcing makes any cardinal superdestructible,” J. Symbolic Logic, vol. 63, iss. 1, pp. 51-58, 1998.
@article {Hamkins98:SmallForcing,
AUTHOR = {Hamkins, Joel David},
TITLE = {Small forcing makes any cardinal superdestructible},
JOURNAL = {J. Symbolic Logic},
FJOURNAL = {The Journal of Symbolic Logic},
VOLUME = {63},
YEAR = {1998},
NUMBER = {1},
PAGES = {51--58},
ISSN = {0022-4812},
CODEN = {JSYLA6},
MRCLASS = {03E40 (03E55)},
MRNUMBER = {1607499 (99b:03068)},
MRREVIEWER = {Jakub Jasi{\'n}ski},
DOI = {10.2307/2586586},
URL = {http://dx.doi.org/10.2307/2586586},
}

• Destruction or preservation as you like it
• J. D. Hamkins, “Destruction or preservation as you like it,” Ann. Pure Appl. Logic, vol. 91, iss. 2-3, pp. 191-229, 1998.
@article {Hamkins98:AsYouLikeIt,
AUTHOR = {Hamkins, Joel David},
TITLE = {Destruction or preservation as you like it},
JOURNAL = {Ann. Pure Appl. Logic},
FJOURNAL = {Annals of Pure and Applied Logic},
VOLUME = {91},
YEAR = {1998},
NUMBER = {2-3},
PAGES = {191--229},
ISSN = {0168-0072},
CODEN = {APALD7},
MRCLASS = {03E55 (03E35)},
MRNUMBER = {1604770 (99f:03071)},
MRREVIEWER = {Joan Bagaria},
DOI = {10.1016/S0168-0072(97)00044-4},
URL = {http://dx.doi.org/10.1016/S0168-0072(97)00044-4},
}

• Every group has a terminating transfinite automorphism tower
• J. D. Hamkins, “Every group has a terminating transfinite automorphism tower,” Proc. Amer. Math. Soc., vol. 126, iss. 11, pp. 3223-3226, 1998.
@article {Hamkins98:EveryGroup,
AUTHOR = {Hamkins, Joel David},
TITLE = {Every group has a terminating transfinite automorphism tower},
JOURNAL = {Proc. Amer. Math. Soc.},
FJOURNAL = {Proceedings of the American Mathematical Society},
VOLUME = {126},
YEAR = {1998},
NUMBER = {11},
PAGES = {3223--3226},
ISSN = {0002-9939},
CODEN = {PAMYAR},
MRCLASS = {20E36 (20F28)},
MRNUMBER = {1487370 (2000e:20057)},
DOI = {10.1090/S0002-9939-98-04797-2},
URL = {http://dx.doi.org/10.1090/S0002-9939-98-04797-2},
eprint = {math/9808014}
}

• Book review of Notes on Set Theory, Moschovakis
• J. D. Hamkins, “book review of Notes on Set Theory, Moschovakis,” Journal of Symbolic Logic, vol. 63, iss. 2, 1998.
@ARTICLE{Hamkins1998:BookReviewMoschovakis,
AUTHOR = "Joel David Hamkins",
TITLE = "book review of {Notes on Set Theory, Moschovakis}",
JOURNAL = "Journal of Symbolic Logic",
YEAR = "1998",
volume = "63",
number = "2",
pages = "",
month = "",
note = "",
abstract = "",
keywords = "",
source = "",
file = F
}

• Canonical seeds and Prikry trees
• J. D. Hamkins, “Canonical seeds and Prikry trees,” J. Symbolic Logic, vol. 62, iss. 2, pp. 373-396, 1997.
@article {Hamkins97:Seeds,
AUTHOR = {Hamkins, Joel David},
TITLE = {Canonical seeds and {P}rikry trees},
JOURNAL = {J. Symbolic Logic},
FJOURNAL = {The Journal of Symbolic Logic},
VOLUME = {62},
YEAR = {1997},
NUMBER = {2},
PAGES = {373--396},
ISSN = {0022-4812},
CODEN = {JSYLA6},
MRCLASS = {03E40 (03E05 03E55)},
MRNUMBER = {1464105 (98i:03070)},
MRREVIEWER = {Douglas R. Burke},
DOI = {10.2307/2275538},
URL = {http://dx.doi.org/10.2307/2275538},
}

• Fragile measurability
• J. Hamkins, “Fragile measurability,” J. Symbolic Logic, vol. 59, iss. 1, pp. 262-282, 1994.
@article {Hamkins94:FragileMeasurability,
AUTHOR = {Hamkins, Joel},
TITLE = {Fragile measurability},
JOURNAL = {J. Symbolic Logic},
FJOURNAL = {The Journal of Symbolic Logic},
VOLUME = {59},
YEAR = {1994},
NUMBER = {1},
PAGES = {262--282},
ISSN = {0022-4812},
CODEN = {JSYLA6},
MRCLASS = {03E35 (03E55)},
MRNUMBER = {1264978 (95c:03129)},
MRREVIEWER = {J. M. Henle},
DOI = {10.2307/2275264},
URL = {http://dx.doi.org/10.2307/2275264},
}

• Lifting and extending measures; fragile measurability
• J. D. Hamkins, “Lifting and extending measures; fragile measurability,” PhD Thesis, University of California, Berkeley, Department of Mathematics, 1994.
@PHDTHESIS{Hamkins94:Dissertation,
author = {Joel David Hamkins},
title = {Lifting and extending measures; fragile measurability},
school = {University of California, Berkeley},
institution = {University of California, Berkeley},
year = {1994},
month = {May},
note = {},
key = {},
annote = {},
}

• A class of strong diamond principles
• J. D. Hamkins, “A class of strong diamond principles,” preprint \hrefhttp://arxiv.org/abs/math/0211419arxiv:math/0211419, 2002.
@ARTICLE{Hamkins:LaverDiamond,
author = {Joel David Hamkins},
title = {A class of strong diamond principles},
journal = {preprint \href{http://arxiv.org/abs/math/0211419}{arxiv:math/0211419}},
year = {2002},
eprint = {math/0211419}
}

• Pointwise definable models of set theory, extended abstract, Oberwolfach 2011
• J. D. Hamkins, “Pointwise definable models of set theory, extended abstract,” Mathematisches Forschungsinstitut Oberwolfach Report, vol. 8, iss. 1, 02/2011, pp. 128-131, 2011.
@ARTICLE{Hamkins2011:PointwiseDefinableModelsOfSetTheoryExtendedAbstract,
AUTHOR = "Joel David Hamkins",
TITLE = "Pointwise definable models of set theory, extended abstract",
JOURNAL = "Mathematisches Forschungsinstitut Oberwolfach Report",
YEAR = "2011",
volume = "8",
number = "1, 02/2011",
pages = "128--131",
month = "",
note = "",
abstract = "",
keywords = "",
source = "",
DOI = {10.4171/OWR/2011/02},
URL = {http://dx.doi.org/10.4171/OWR/2011/02},
file = F
}

## 2 thoughts on “Publications”

1. It seems that infinite time Turing machines are fully deterministic except at the limit stages when cells on the tape are updated to the lim sup of a countable infinity of values that occurred in the cells at non-limit stages. What kind of hardware would we have to imagine added to an ordinary Turing machine to complete the analysis that determines this lim sup for each cell? In other words, how could a machine be built to discover whether the series of cell contents converges to 1 or oscillates continually between 0 and 1?

• The limit cell values are deterministic in the sense that the value at the limit is logically determined by earlier values, and it couldn’t be a different value (contrast with non-deterministic computation in finite time, where there is a sense in which the next step of computation is not logically determined by the previous states, since there are multiple paths of computation that all accord with the computational rules). As for the physical implementation, this is an issue for the physicists. I imagine some kind of biased magnetic cell memory, which will show a positive value at a limit if it was unboundedly often positive going in to the limit. Ultimately, of course, what I am interested in is the purely mathematical theory of the resulting class of functions, and so the issue of physical implementation doesn’t actually matter.