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,...
View ArticleIs the twin prime conjecture independent of Peano Arithmetic?
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View ArticleTransfinite game values in infinite draughts
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View ArticleInfinite Hex is a draw
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View ArticleInfinite Wordle and the Mastermind numbers
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View ArticleReflection in second-order set theory with abundant urelements bi-interprets...
[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...
View ArticleNonlinearity and illfoundedness in the hierarchy of large cardinal...
[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...
View ArticleFregean abstraction in Zermelo-Fraenkel set theory: a deflationary account
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View ArticleEvery countable model of arithmetic or set theory has a pointwise definable...
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View ArticleSelf-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...
View ArticlePseudo-countable models
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View ArticleSet 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...
View ArticleA deflationary account of Fregean abstraction in set theory, with Basic Law V...
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,...
View ArticleDid 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. Continue reading →
View ArticleHow 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. Continue reading →
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