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

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

Reviews of my publications are available on

• MathScinet
• Zentralblatt

See also

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

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

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

• How the continuum hypothesis could have been a fundamental axiom

  Joel David Hamkins, “How the continuum hypothesis could have been a fundamental axiom,” Mathematics arXiv (2024), arxiv:2407.02463.

• Did Turing prove the undecidability of the halting problem?

  Joel David Hamkins and Theodor Nenu, “Did Turing prove the undecidability of the halting problem?”, 18 pages, 2024, arxiv:2407.00680.

• A deflationary account of Fregean abstraction in set theory, with Basic Law V as a ZFC theorem, Paris PhilMath Intersem 2023

  This will be a talk for the Axe Histoire et Philosophie des mathématiques, Séminaire PhilMath Intersem 2023,  a collaborative event sponsored by the University of Notre Dame and le laboratoire SPHERE, Paris. The Intersem runs several weeks, but my talk …

• Set theory with abundant urelements, STUK 10, Oxford, June 2023

  This will be a talk for the Set Theory in the UK, STUK 10, held in Oxford 14 June 2023, organized by my students Clara List, Emma Palmer, and Wojciech Wołoszyn. Abstract. I shall speak on the surprising strength of …

• Pseudo-countable models

  [bibtex key=”Hamkins:Pseudo-countable-models”]

• Self-similar self-similarity, in The Language of Symmetry

  A playful account of symmetry, contributed as a chapter to a larger work, The Language of Symmetry, edited by Benedict Rattigan, Denis Noble, and Afiq Hatta, a collection of essays on symmetry that were also the basis of an event …

• Every countable model of arithmetic or set theory has a pointwise definable end extension

  [bibtex id=”Hamkins:Every-countable-model-of-arithmetic-or-set-theory-has-a-pointwise-definable-end-extension”]

• Fregean abstraction in Zermelo-Fraenkel set theory: a deflationary account

  [bibtex key=”Hamkins:Fregean-abstraction-deflationary-account”]

• Nonlinearity and illfoundedness in the hierarchy of large cardinal consistency strength

  [bibtex key=”Hamkins:Nonlinearity-in-the-hierarchy-of-large-cardinal-consistency-strength”] arXiv:2208.07445 Abstract. Many set theorists point to the linearity phenomenon in the hierarchy of consistency strength, by which natural theories tend to be linearly ordered and indeed well ordered by consistency strength. Why should it be linear? In …

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

  [bibtex key=”HamkinsYao:Reflection-in-second-order-set-theory-with-abundant-urelements”] Download pdf at arXiv:2204.09766 Abstract. After reviewing various natural bi-interpretations in urelement set theory, including second-order set theories with urelements, we explore the strength of second-order reflection in these contexts. Ultimately, we prove, second-order reflection with the abundant …

• Infinite Wordle and the Mastermind numbers

  [bibtex key=”Hamkins:Infinite-Wordle-and-the-mastermind-numbers”]

• Infinite Hex is a draw

  [bibtex key=”HamkinsLeonessi:Infinite-Hex-is-a-draw”]

• Transfinite game values in infinite draughts

  [bibtex key=”HamkinsLeonessi:Transfinite-game-values-in-infinite-draughts”]

• Is the twin prime conjecture independent of Peano Arithmetic?

  [bibtex key=”BerarducciFornasieroHamkins:Is-the-twin-prime-conjecture-independent-of-PA”]

• Book review, Catarina Dutilh Novaes, The dialogical roots of deduction

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

• Nonlinearity in the hierarchy of large cardinal consistency strength

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

• Proof and the Art of Mathematics: Examples and Extensions

  A companion volume to my proof-writing book, Proof and the Art of Mathematics. [bibtex key=”Hamkins2021:Proof-and-the-art-examples”] Now available! Book profile at MIT Press Amazon.com Amazon.co.uk Order through your local bookstore Follow the conversation on Twitter via #ProofandtheArt From the Preface: The …

• Lectures on the Philosophy of Mathematics

  [bibtex key=”Hamkins2021:Lectures-on-the-philosophy-of-mathematics”]

• Modal model theory

  [bibtex key=”HamkinsWoloszyn:Modal-model-theory”]

• Categorical large cardinals and the tension between categoricity and set-theoretic reflection

  [bibtex key=”HamkinsSolberg:Categorical-large-cardinals”]

• Choiceless large cardinals and set-theoretic potentialism

  [bibtex key=”CutoloHamkins:Choiceless-large-cardinals-and-set-theoretic-potentialism”]

• Forcing as a computational process

  [bibtex key=”HamkinsMillerWilliams:Forcing-as-a-computational-process”]

• My view of Univ

  [bibtex key=”Hamkins2020:My-view-of-univ”]

• Proof and the Art of Mathematics

  [bibtex key=”Hamkins2020:Proof-and-the-art-of-mathematics”]

• Bi-interpretation in weak set theories

  [bibtex key=”FreireHamkins:Bi-interpretation-in-weak-set-theories”]

• The $\Sigma_1$-definable universal finite sequence

  [bibtex key=”HamkinsWilliams2021:The-universal-finite-sequence”]

• Representing Ordinal Numbers with Arithmetically Interesting Sets of Real Numbers

  [bibtex key=”BlairHamkinsOBryant2020:Representing-ordinal-numbers-with-arithmetically-interesting-sets-of-real-numbers”]

• Kelley-Morse set theory does not prove the class Fodor principle

  [bibtex key=”GitmanHamkinsKaragila:KM-set-theory-does-not-prove-the-class-Fodor-theorem”]

• 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

  [bibtex key=”HabicHamkinsKlausnerVernerWilliams2018:Set-theoretic-blockchains”]

• Topological models of arithmetic

  [bibtex key=”EnayatHamkinsWcislo2021:Topological-models-of-arithmetic”]

• Open class determinacy is preserved by forcing

  [bibtex key=”HamkinsWoodin2018:Open-class-determinacy-is-preserved-by-forcing”]

• The subseries number

  [bibtex key=”BrendleBrianHamkins2019:The-subseries-number”]

• The modal logic of arithmetic potentialism and the universal algorithm

  [bibtex key=”Hamkins:The-modal-logic-of-arithmetic-potentialism”]

• The universal finite set

  [bibtex key=”HamkinsWoodin:The-universal-finite-set”]

• The set-theoretic universe is not necessarily a class-forcing extension of HOD

  [bibtex key=”HamkinsReitz:The-set-theoretic-universe-is-not-necessarily-a-forcing-extension-of-HOD”]

• Inner-model reflection principles

  [bibtex key=”BartonCaicedoFuchsHamkinsReitzSchindler2020:Inner-model-reflection-principles”]

• The modal logic of set-theoretic potentialism and the potentialist maximality principles

  [bibtex key=”HamkinsLinnebo:Modal-logic-of-set-theoretic-potentialism”]

• Boolean ultrapowers, the Bukovský-Dehornoy phenomenon, and iterated ultrapowers

  [bibtex key=”FuchsHamkins:TheBukovskyDehornoyPhenomenonForBooleanUltrapowers”]

• The exact strength of the class forcing theorem

  [bibtex key=”GitmanHamkinsHolySchlichtWilliams2020:The-exact-strength-of-the-class-forcing-theorem”]

• When does every definable nonempty set have a definable element?

  [bibtex key=”DoraisHamkins:When-does-every-definable-nonempty-set-have-a-definable-element”]

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

  [bibtex key=”GitmanHamkins2018:A-model-of-the-generic-Vopenka-principle-in-which-the-ordinals-are-not-Mahlo”]

• The inclusion relations of the countable models of set theory are all isomorphic

  [bibtex key=”HamkinsKikuchi:The-inclusion-relations-of-the-countable-models-of-set-theory-are-all-isomorphic”]

• Computable quotient presentations of models of arithmetic and set theory

  [bibtex key=GodziszewskiHamkins2017:Computable-quotient-presentations-of-models-of-arithmetic-and-set-theory]

• The implicitly constructible universe

  [bibtex key=”GroszekHamkins2019:The-implicitly-constructible-universe”]

• The rearrangement number

  [bibtex key=BlassBrendleBrianHamkinsHardyLarson2020:TheRearrangementNumber]

• Ord is not definably weakly compact

  [bibtex key=EnayatHamkins2018:Ord-is-not-definably-weakly-compact]

• The Vopěnka principle is inequivalent to but conservative over the Vopěnka scheme

  [bibtex key=Hamkins:The-Vopenka-principle-is-inequivalent-to-but-conservative-over-the-Vopenka-scheme]

• Set-theoretic mereology

  [bibtex key=HamkinsKikuchi2016:Set-theoreticMereology]

• Upward closure and amalgamation in the generic multiverse of a countable model of set theory

  [bibtex key=Hamkins2016:UpwardClosureAndAmalgamationInTheGenericMultiverse]

• A position in infinite chess with game value $\omega^4$

  [bibtex key=EvansHamkinsPerlmutter2017:APositionInInfiniteChessWithGameValueOmega^4]

• Open determinacy for class games

  [bibtex key=GitmanHamkins2016:OpenDeterminacyForClassGames]

• A mathematician’s year in Japan

  [bibtex key=Hamkins2015:AMathematiciansYearInJapan]

• Ehrenfeucht’s lemma in set theory

  [bibtex key=FuchsGitmanHamkins2018:EhrenfeuchtsLemmaInSetTheory]

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

  [bibtex key=FuchsGitmanHamkins2017:IncomparableOmega1-likeModelsOfSetTheory]

• Large cardinals need not be large in HOD

  [bibtex key=ChengFriedmanHamkins2015:LargeCardinalsNeedNotBeLargeInHOD]

• Strongly uplifting cardinals and the boldface resurrection axioms

  [bibtex key=HamkinsJohnstone2017:StronglyUpliftingCardinalsAndBoldfaceResurrection]

• Satisfaction is not absolute

  [bibtex key=HamkinsYang:SatisfactionIsNotAbsolute]

• The foundation axiom and elementary self-embeddings of the universe

  [bibtex key=DaghighiGolshaniHaminsJerabek2013:TheFoundationAxiomAndElementarySelfEmbeddingsOfTheUniverse]

• Resurrection axioms and uplifting cardinals

  [bibtex key=HamkinsJohnstone2014:ResurrectionAxiomsAndUpliftingCardinals]

• Superstrong and other large cardinals are never Laver indestructible

  [bibtex key=BagariaHamkinsTsaprounisUsuba2016:SuperstrongAndOtherLargeCardinalsAreNeverLaverIndestructible]

• The least weakly compact cardinal can be unfoldable, weakly measurable and nearly $\theta$-supercompact

  [bibtex key=CodyGitikHamkinsSchanker2015:LeastWeaklyCompact]

• Algebraicity and implicit definability in set theory

  [bibtex key=HamkinsLeahy2016:AlgebraicityAndImplicitDefinabilityInSetTheory]

• Transfinite game values in infinite chess

  [bibtex key=EvansHamkins2014:TransfiniteGameValuesInInfiniteChess]

• A multiverse perspective on the axiom of constructiblity

  [bibtex key=Hamkins2014:MultiverseOnVeqL]

• 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

  [bibtex key=HamkinsLoewe2013:MovingUpAndDownInTheGenericMultiverse]

• Structural connections between a forcing class and its modal logic

  [bibtex key=HamkinsLeibmanLoewe2015:StructuralConnectionsForcingClassAndItsModalLogic]

• Every countable model of set theory embeds into its own constructible universe

  [bibtex key=Hamkins2013:EveryCountableModelOfSetTheoryEmbedsIntoItsOwnL]

• Well-founded Boolean ultrapowers as large cardinal embeddings

  [bibtex key=HamkinsSeabold:BooleanUltrapowers]

• Singular cardinals and strong extenders

  [bibtex key=ApterCummingsHamkins2013:SingularCardinalsAndStrongExtenders]

• Is the dream solution of the continuum hypothesis attainable?

  [bibtex key=Hamkins2015:IsTheDreamSolutionToTheContinuumHypothesisAttainable]

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

  [bibtex key=BrumleveHamkinsSchlicht2012:TheMateInNProblemOfInfiniteChessIsDecidable]

• Inner models with large cardinal features usually obtained by forcing

  [bibtex key=ApterGitmanHamkins2012:InnerModelsWithLargeCardinals]

• What is the theory ZFC without power set?

  [bibtex key=”GitmanHamkinsJohnstone2016:WhatIsTheTheoryZFC-Powerset?”]

• The hierarchy of equivalence relations on the natural numbers under computable reducibility

  [bibtex key=CoskeyHamkinsMiller2012:HierarchyOfEquivalenceRelationsOnN]

• Set-theoretic geology

  [bibtex key=FuchsHamkinsReitz2015:Set-theoreticGeology]

• The rigid relation principle, a new weak choice principle

  [bibtex key=HamkinsPalumbo2012:TheRigidRelationPrincipleANewWeakACPrinciple]

• Generalizations of the Kunen inconsistency

  [bibtex key=HamkinsKirmayerPerlmutter2012:GeneralizationsOfKunenInconsistency]

• Pointwise definable models of set theory

  [bibtex key=HamkinsLinetskyReitz2013:PointwiseDefinableModelsOfSetTheory]

• Effective Mathemematics of the Uncountable

  [bibtex key=EMU]

• Infinite time Turing machines and an application to the hierarchy of equivalence relations on the reals

  [bibtex key=CoskeyHamkins2013:ITTMandApplicationsToEquivRelations]

• The set-theoretical multiverse

  [bibtex key=Hamkins2012:TheSet-TheoreticalMultiverse]

• Infinite time decidable equivalence relation theory

  [bibtex key=CoskeyHamkins2011:InfiniteTimeComputableEquivalenceRelations]

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

  [bibtex key=Hamkins2011:TheMultiverse:ANaturalContext]

• A natural model of the multiverse axioms

  [bibtex key=GitmanHamkins2010:NaturalModelOfMultiverseAxioms]

• Indestructible strong unfoldability

  [bibtex key=HamkinsJohnstone2010:IndestructibleStrongUnfoldability]

• Some second order set theory

  [bibtex key=Hamkins2009:SomeSecondOrderSetTheory]

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

  [bibtex key=HamkinsMiller2009:PostsProblemForORMsExplicitApproach]

• Degrees of rigidity for Souslin trees

  [bibtex key=FuchsHamkins2009:DegreesOfRigidity]

• Tall cardinals

  [bibtex key=Hamkins2009:TallCardinals]

• The proper and semi-proper forcing axioms for forcing notions that preserve $\aleph_2$ or $\aleph_3$

  [bibtex key=HamkinsJohnstone2009:PFA(aleph_2-preserving)]

• Infinite time computable model theory

  [bibtex key=HamkinsMillerSeaboldWarner2007:InfiniteTimeComputableModelTheory]

• Changing the heights of automorphism towers by forcing with Souslin trees over $L$

  [bibtex key=FuchsHamkins2008:ChangingHeightsOverL]

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

  [bibtex key=HamkinsReitzWoodin2008:TheGroundAxiomAndVequalsHOD]

• The modal logic of forcing

  [bibtex key=HamkinsLoewe2008:TheModalLogicOfForcing]

• Large cardinals with few measures

  [bibtex key=ApterCummingsHamkins2006:LargeCardinalsWithFewMeasures]

• A survey of infinite time Turing machines

  [bibtex key=Hamkins2007:ASurveyOfInfiniteTimeTuringMachines]

• The complexity of quickly decidable ORM-decidable sets

  [bibtex key=HamkinsLinetskyMiller2007:ComplexityOfQuicklyDecidableORMSets]

• Post's Problem for Ordinal Register Machines

  [bibtex key=HamkinsMiller2007:PostsProblemForORMs]