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## May 19, 2025: How we might have viewed the continuum hypothesis as a fundamental axiom necessary for mathematics, Oxford Phil Maths seminar, May 2025

This will be a talk for the Philosophy of Mathematics Seminar at the University of Oxford, 19 May 2025. Abstract. I shall describe a simple historical thought experiment showing how our attitude toward the continuum hypothesis could easily have been very different … Continue reading

postlist:

- Infinite-time computable analogues of the universal algorithm, Generalized Computability Theory Workshop, Spain, August 2014
This will be a talk at the Generalized Computability Theory workshop in Castro Urdiales, Spain, a beautiful setting on the sea near Bilbao, 19-23 August 2024. Abstract. I shall present infinite-time computable analogues of the universal algorithm, which can in …

- How we might have viewed the continuum hypothesis as a fundamental axiom necessary for mathematics, Oxford Phil Maths seminar, May 2025
This will be a talk for the Philosophy of Mathematics Seminar at the University of Oxford, 19 May 2025. Abstract. I shall describe a simple historical thought experiment showing how our attitude toward the continuum hypothesis could easily have been very different …

- Puzzles of reality and infinity, Mindscape Podcast
I was interviewed by Sean Carroll for his Mindscape Podcast, broadcast 15 July 2024.

- Mathematics, Philosophy of Set Theory and Infinity, Back to the Stone Age interview, May 2024
I was interviewed by Francesco Cavina for the Back to the Stone Age series on May 17, 2024, with a sweeping discussion of the philosophy of set theory, infinity, the continuum hypothesis, beauty in mathematics, and much more.

- Life Story of Mathematician & Philosopher of Infinity, interviewed by The Human Podcast, May 2024
I was interviewed by The Human Podcast on 17 May 2024. Please enjoy our sweeping conversation about nature of infinity, the nature of abstract mathematical existence, the applicability of mathematical abstractions to physical reality, and more. At the end, you …

- Forcing is simply the iterative conception undertaken with multivalued logic, ForcingFest, Oslo, June 2024
I shall be speaking at the ForcingFest meeting at the University of Oslo, 21 June 2024. Abstract. I will explain how the forcing construction can be seen as a direct implementation of the iterative conception, giving rise to the cumulative …

- The continuum hypothesis could have been a fundamental axiom, CFORS Grad Conference, Oslo, June 2024
I shall be giving a keynote lecture for the CFORS Grad Conference at the University of Oslo, 19-20 June 2024. Abstract. I shall describe a simple historical thought experiment showing how our attitude toward the continuum hypothesis could easily have been very …

- Failing definite descriptions, Notre Dame Food for Thought Seminar, March 2024
I gave a talk for the Food for Thought seminar for the Notre Dame philosophy department. The topic concerned definite descriptions, particularly the semantics that might be given when one extends first-order logic to include the iota operator, by which …

- How the continuum hypothesis could have been a fundamental axiom, UC Irvine Logic & Philosoph of Science Colloquium, March 2024
This will be a talk for the Logic and Philosophy of Science Colloquium at the University of California at Irvine, 15 March 2024. Abstract. With a simple historical thought experiment, I should like to describe how we might easily have …

- What if your potentialism is implicitly actualist? Oxford conference, March 2024
This will be a talk at the conference Challenging the Infinite, March 11-12 at Oxford University. (Please register now to book a place.) Abstract Many commonly considered forms of potentialism, I argue, are implicitly actualist in the sense that a …

- The covering reflection principle, Notre Dame Logic Seminar, February 2024
This will be a talk for the Notre Dame Logic Seminar on 6 February 2024, 2:00 pm. Abstract. The principle of covering reflection holds of a cardinal $\kappa$ if for every structure $B$ in a countable first-order language there is …

- The Gödel incompleteness phenomenon, interview with Rahul Sam
Please enjoy my conversation with Rahul Sam for his podcast, a sweeping discussion of topics in the philosophy of mathematics—potentialism, pluralism, Gödel incompleteness, philosophy of set theory, large cardinals, and much more.

- Pluralism in the foundations of mathematics, ASL invited address, joint APA/ASL meeting, New York, January 2024
This will be an invited ASL address at the joint meeting of the ASL with the APA Eastern Division conference, held in New York 15-18 January 2024. My talk will be 16 January 2024 11:00 am. Abstract. I shall give …

- The computable model theory of forcing, Rutgers Logic Seminar, December 2023
This will be a talk for the Rutgers University Logic Seminar, December 4, 2023. Abstract. I shall discuss the computable model theory of forcing. To what extent can we view forcing as a computational process on the models of set …

- The Wordle and Absurdle numbers, CUNY Logic Workshop, November 2023
This will be a talk for the CUNY Logic Workshop, 17 November 2023. Abstract. We consider the game of infinite Wordle as played on Baire space $\omega^\omega$. The codebreaker can win in finitely many moves against any countable dictionary $\Delta\subseteq\omega^\omega$, …

- What is second-order predicate modal logic? FoMoLo Seminar, February 2024
This will be a talk for the First-order Modal Logic (FoMoLo) Seminar, 12 February 2024. The talk will take place online via Zoom—contact the organizers for access. Abstract. What is or should be the potentialist account of classes? There are …

- The surprising strength of second-order reflection in urelement set theory, Luminy, October 2023
This will be a talk at the XVII International Luminy Workshop in Set Theory at the Centre International de Rencontres Mathématiques (CIRM) near Marseille, France, held 9-13 October 2023. Abstract. I shall give a general introduction to urelement set theory …

- What is potentialist second-order logic? Konstanz Actualism and Potentialism Conference 2023
This is a talk for the Actualism and Potentialism Conference at the University of Konstanz, 28-29 September 2023. Also on Zoom: 928 0804 3434. Abstract. What is or should be the potentialist account of classes? It turns out that there …

- Infinite-Games Workshop
Welcome to the Infinite-Games Workshop, beginning Autumn 2023. The past ten years has seen an explosion in the study of infinite games, for researchers are now investigating diverse infinite games, including infinite chess, infinite draughts, infinite Hex, infinite Othello, infinite …

- Philosophy of Mathematics and Truth, interview with Matthew Geleta on Paradigm Podcast
We had a sweeping discussion touching upon many issues in the philosophy of mathematics, including the nature of mathematical truth, mathematical abstraction, the nature of mathematical existence, the meaning and role of proof in mathematics, the completeness theorem, the incompleteness …

- An exploration of infinite games—infinite Wordle and the Mastermind numbers, Harvard, October 2023
This will be a talk 16 October 2023 (Note new date!) for the Colloquium of the Harvard Center for Mathematical Sciences and Applications (CMSA). Abstract: Let us explore the nature of strategic reasoning in infinite games, focusing on the cases of …

- Natural Instances of Illfoundedness and Nonlinearity in the Hierarchy of Consistency Strength, Oxford Phil Math Seminar, May 2023
Abstract. There is an unexplained logical mystery in the foundations of mathematics, namely, our best and strongest mathematical theories seem to be linearly ordered and indeed well-ordered by consistency strength. Why should it be? The phenomenon is thought to carry …

- How to find pointwise definable and Leibnizian extensions of models of arithmetic and set theory, Oxford Logic Seminar, May 2023
This will be a talk (in person) for the Logic Seminar of the Mathematics Institute of the Univerisity of Oxford, May 18, 2023 5pm, Wiles Building L3. Abstract: I shall present a new flexible method showing that every countable model of …

- Infinite games—strategies, logic, theory, and computation, Northeastern, June 2023
This will be an online Zoom talk for the Boston Computaton Club, a graduate seminar in computer science at Northeastern University, 16 June 12pm EST (note change in date/time). Contact the organizers for the Zoom link. Abstract: Many familiar finite …

- Realizing Frege’s Basic Law V provably in ZFC, New York, May 2023
This will be a talk for the CUNY Set Theory Seminar on May 5, 2023 10am. Contact the organizers for the Zoom link. Abstract. The standard set-theoretic distinction between sets and classes instantiates in important respects the Fregean distinction between …

- Set-theoretic forcing as a computational process, Midwest Computability Seminar, Chicago, May 2023
This is a talk for the MidWest Computability Seminar conference held May 2, 2023 at the University of Chicago. The talk will be available via Zoom at https://notredame.zoom.us/j/99754332165?pwd=RytjK1RFZU5KWnZxZ3VFK0g4YTMyQT09. Abstract: I shall explore several senses in which set-theoretic forcing can be …

- Varieties of potentialism, Oslo, April 2023
This will be an online talk for the Infinity & Intentionality project of Øystein Linnebo in Oslo, 25 April 2023. Zoom link available from the organizers. Abstract: I shall survey the surprisingly enormous variety of potentialist conceptions, even in the …

- Natures of Proof, Pacific APA, San Francisco, April 2023
I am a commentator at the Pacific APA 2023 conference in San Francisco in a Book Symposium session focused on the book of Catarina Duthil Novaes, The Dialogical Roots of Deduction. I think very highly of Novaes’s book (my book …

- Pointwise definable and Leibnizian extensions of models of arithmetic and set theory, Madison Logic Seminar, April 2023
Abstract. I shall present a new flexible method showing that every countable model of PA admits a pointwise definable-elementary end-extension. Also, any model of PA of size at most continuum admits an extension that is Leibnizian, meaning that any two …

- The Math Tea argument: must there be numbers we can neither describe nor define? Barcelona March 2023
This will be a talk 15 March 2023 for the Mathematics Department of the University of Barcelona, organized jointly with the Set Theory Seminar. Abstract. According to the math tea argument, perhaps heard at a good afternoon tea,there must be …

- A survey of set-theoretic geology, Notre Dame Logic Seminar, January 2023
This will be a talk 31 January 2-3 for the Notre Dame Logic Seminar. Abstract. I shall give a general introduction and account of the main elements of set-theoretic geology, the motivating questions, the central definitions, and the main results, …

- Paradox, Infinity, & The Foundations of Mathematics, interview with Robinson Erhardt, January 2023
This was an interview with Robinson Erhardt on Robinson’s Podcast, part of his series of interviews with various philosophers, including many philosophers of mathematics and more. We had a wonderfully wide-ranging discussion about the philosophy of mathematics, the philosophy of …

- Strategic thinking in infinite games, CosmoCaixa Science Museum, Barcelona, March 2023
I am deeply honored to be invited by la Caixa Foundation to give a talk in “The Greats of Science” talk series, to be held 16 March 2023 at the CosmoCaixa Science Museum in Barcelona. This talk series aspires to …

- Pointwise definable and Leibnizian extensions of models of arithmetic and set theory, MOPA seminar CUNY, November 2022
This will be an online talk for the MOPA Seminar at CUNY on 22 November 2022 1pm. Contact organizers for Zoom access. Abstract. I shall introduce a flexible new method showing that every countable model of PA admits a pointwise …

- Pointwise definable and Leibnizian models of arithmetic and set theory, realized in end extensions of a given model, Notre Dame Logic Seminar, October 2022
This will be a talk for the Notre Dame logic seminar, 11 October 2022, 2pm in Hales-Healey Hall. Abstract. I shall present very new results on pointwise definable and Leibnizian end-extensions of models of arithmetic and set theory. Using the …

- The math tea argument—must there be numbers we cannot describe or define? Pavia Logic Seminar
This will be a talk for the Philosophy Seminar at the IUSS, Scuola Universitaria Superiore Pavia, 28 September 2022. (Note: This seminar will be held the day before the related conference Philosophy of Mathematics: Foundations, Definitions and Axioms, Italian Network …

- Workshop on the Set-theoretic Multiverse, Konstanz, September 2022
Masterclass of “The set-theoretic multiverse” ten years after Focused on mathematical and philosophical aspects of the set-theoretic multiverse and the pluralist debate in the philosophy of set theory, this workshop will have a master class on potentialism, a series of …

- Pointwise definable end-extensions of the universe, Sophia 2022, Salzburg
This will be an online talk for the Salzburg Conference for Young Analytical Philosophy, the SOPhiA 2022 Salzburgiense Concilium Omnibus Philosophis Analyticis, with a special workshop session Reflecting on ten years of the set-theoretic multiverse. The workshop will meet Thursday …

- Fregean abstraction in set theory—a deflationary account, Italian Philosophy of Mathematics, September 2022
This will be a talk for the conference Philosophy of Mathematics: Foundations, Definitions and Axioms, the Fourth International Conference of the Italian Network for the Philosophy of Mathematics, 29 September to 1 October 2022. Abstract. The standard set-theoretic distinction between …

- Nonlinearity and illfoundedness in the hierarchy of consistency strength and the question of naturality, Italy (AILA), September 2022
This will be a talk for the meeting of The Italian Association for Logic and its Applications (AILA) in Caserta, Italy 12-15 September 2022. Abstract. Set theorists and philosophers of mathematics often point to a mystery in the foundations of …

- Set theory inside out: realizing every inner model theory in an end extension, European Set Theory Conference, September 2022
This will be a talk for the European Set Theory Conference 2022 in Turin, Italy 29 August – 2 September 2022. Abstract. Every countable model of ZFC set theory with an inner model satisfying a sufficient theory must also have …

- The ontology of mathematics, Japan Association for the Philosophy of Science, June 2022
I shall give the Invited Lecture for the Annual Meeting (online) of the Japanese Association for the Philosophy of Science, 18-19 June 2022. Abstract. What is the nature of mathematical ontology—what does it mean to make existence assertions in mathematics? …

- Infinite Games, Frivolities of the Gods, Logic at Large Lecture, May 2022
The Dutch Association for Logic and Philosophy of the Exact Sciences (VvL) has organized a major annual public online lecture series called LOGIC AT LARGE, where “well-known logicians give public audience talks to a wide audience,” and I am truly …

- The surprising strength of reflection in second-order set theory with abundant urelements, CUNY Set Theory seminar, April 2022
This was an online talk 15 April 12:15 for the CUNY Set Theory Seminar. Held on Zoom at 876 9680 2366. Abstract. I shall give a general introduction to urelement set theory and the role of the second-order reflection principle …

- Infinite Wordle and the mastermind numbers, CUNY Logic Workshop, March 2022
This will be an in-person talk for the CUNY Logic Workshop at the Graduate Center of the City University of New York on 11 March 2022. Abstract. I shall introduce and consider the natural infinitary variations of Wordle, Absurdle, and …

- Pluralism in the ontology of mathematics, MaMuPhi, Paris, February 2022
This will be a talk for the conference L’indépendance mathématique et ses limites logiques, an instance of the MAMUPHI seminar (mathématiques – musique – philosophie), organized by Mirna Džamonja, 12 February 2022. Most talks will be in-person in Paris, but my talk …

- The model theory of set-theoretic mereology, Notre Dame Math Logic Seminar, February 2022
This will be a talk for the Mathematical Logic Seminar at the University of Notre Dame on 8 February 2022 at 2 pm in 125 Hayes Healy. Abstract. Mereology, the study of the relation of part to whole, is often …

- Bi-interpretation in set theory, Oberwolfach Set Theory Conference, January 2022
This was a talk for the 2022 Set Theory Conference at Oberwolfach, which was a hybrid of in-person talks and online talks on account of the Covid pandemic. I gave my talk online 10 January 2022. Abstract: Set theory exhibits …

- The surprising strength of reflection in second-order set theory with abundant urelements, Konstanz, December 2021
This will be talk for the workshop Philosophy of Set Theory held at the University of Konstanz, 3 – 4 December 2021 — in person! Update: Unfortunately, the workshop has been cancelled (perhaps postponed to next year) in light of …

- Infinite draughts and the logic of infinitary games, Oslo, November 2021
This will be a talk 11 November 2021 for the Oslo Seminar in Mathematical Logic, meeting online via Zoom at 10:15am CET (9:15am GMT) at Zoom: 671 7500 0197 Abstract. I shall give an introduction to the logic of infinite …

- Frege’s philosophy of mathematics—Interview with Nathan Ormond, December 2021
I was interviewed by Nathan Ormond for a discussion on Frege’s philosophy of mathematics for his YouTube channel, Digital Gnosis, on 10 December 2021 at 4pm. The interview concludes with a public comment and question & answer session.

- A deflationary account of Fregean abstraction in Zermelo-Fraenkel ZF set theory, Oxford, November 2021
This will be a talk for the Oxford Seminar in the Philosophy of Mathematics, 1 November, 4:30-6:30 GMT. The talk will be held on Zoom (contact the seminar organizers for the Zoom link). Abstract. The standard treatment of sets and …

- My favorite theorem
What a pleasure it was to be interviewed by Evelyn Lamb and Kevin Knudson for their wonderful podcast series, My Favorite Theorem, available on Apple, Spotify, and any number of other aggregators. I had a chance to talk about one …

- Infinite sets and Foundations—Interviewed on the Daniel Rubin Show
I was interviewed 26 August 2021 by mathematician Daniel Rubin on his show, and we had a lively, wideranging discussion spanning mathematics, infinity, and the philosophy of mathematics. Please enjoy! Contents 0:00 Intro 2:11 Joel’s background. Interaction between math and …

- The Tennenbaum phenomenon for computable quotient presentations of models of arithmetic and set theory, Shanghai, August 2021
This will be a talk for the conference Fudan Model Theory and Philosophy of Mathematics, held at Fudan University in Shanghai and online, 21-24 August 2021. My talk will take place on Zoom on 23 August 20:00 Beijing time (1pm …

- Naturality in mathematics and the hierarchy of consistency strength, University of Konstanz, July 2021
This is a talk for the Logik Kolloquium at the University of Konstanz, spanning the departments of mathematics, philosophy, linguistics, and computer science. 19 July 2021 on Zoom. 15:15 CEST (2:15 pm BST). Abstract: An enduring mystery in the …

- Categorical set theories, Munich, June 2021
This is a talk for the group in logic and philosophy of language at the Munich Center for Mathematical Philosophy 24 June 2021, 4:15 pm Munich time (3:15 pm BST) on Zoom at 925 6562 2309 (contact Ursula Danninger office.leitgeb@lrz.uni-muenchen.de …

- Potentialism and implicit actualism in the foundations of mathematics, Notre Dame, March 2021
This will be a talk for the Department Colloquium of the Philosophy Department of the University of Notre Dame, 26 March 12 pm EST (4pm GMT). Abstract: Potentialism is the view, originating in the classical dispute between actual and potential …

- Reading and discussion of Lectures on the Philosophy of Mathematics, Amsterdam, March 2021
This will be an event for the $\Phi$-Math Reading Group at the Institute for Logic, Language, and Computation (ILLC) at the University of Amsterdam, 19 March 2021 6pm CET (5pm GMT). Zoom access here. I shall make a brief presentation …

- Forcing as a computational process, Kobe Set Theory Workshop, March 2021
This was a talk for the Kobe Set Theory Workshop, held on the occasion of Sakaé Fuchino’s retirement, 9-11 March 2021. Abstract. I shall discuss senses in which set-theoretic forcing can be seen as a computational process on the models …

- Determinacy for proper class games, Seminaire de Logique Lyon-Paris, April 2021
This will be a talk for the Seminaire de Logique Lyon-Paris on 14 April 2021 4pm Paris time (3pm UK). The talk will be held on Zoom at 875 1148 7359. Abstract. The principle of open determinacy for class games …

- Definability and the Math Tea argument: must there be numbers we cannot describe or define? University of Warsaw, 22 January 2021
This will be a talk for a new mathematical logic seminar at the University of Warsaw in the Department of Hhilosophy, entitled Epistemic and Semantic Commitments of Foundational Theories, devoted to formal truth theories and implicit commitments of foundational theories …

- Can there be natural instances of nonlinearity in the hierarchy of consistency strength? UWM Logic Seminar, January 2021
This is a talk for the University of Wisconsin, Madison Logic Seminar, 25 January 2020 1 pm (7 pm UK). The talk will be held online via Zoom ID: 998 6013 7362. Abstract. It is a mystery often mentioned in …

- Set-theoretic and arithmetic potentialism: the state of current developments, CACML 2020
This will be a plenary talk for the Chinese Annual Conference on Mathematical Logic (CACML 2020), held online 13-15 November 2020. My talk will be held 14 November 17:00 Beijing time (9 am GMT). Abstract. Recent years have seen a …

- Continuous models of arithmetic, MOPA, November 2020
This will be a talk for the Models of Peano Arithmetic (MOPA) seminar on 11 November 2020, 12 pm EST (5pm GMT). Kindly note the rescheduled date and time. Abstract. Ali Enayat had asked whether there is a model of …

- A new proof of the Barwise extension theorem, and the universal finite sequence, Barcelona Set Theory Seminar, 28 October 2020
This will be a talk for the Barcelona Set Theory Seminar, 28 October 2020 4 pm CET (3 pm UK). Contact Joan Bagaria bagaria@ub.edu for the access link. Abstract. The Barwise extension theorem, asserting that every countable model of ZF …

- Modal model theory as mathematical potentialism, Oslo online Potentialism Workshop, September 2020
This will be a talk for the Oslo potentialism workshop, Varieties of Potentialism, to be held online via Zoom on 23 September 2020, from noon to 18:40 CEST (11am to 17:40 UK time). My talk is scheduled for 13:10 CEST …

- Categorical cardinals, CUNY Set Theory Seminar, June 2020
This will be an online talk for the CUNY Set Theory Seminar, Friday 26 June 2020, 2 pm EST = 7 pm UK time. Contact Victoria Gitman for Zoom access. Abstract: Zermelo famously characterized the models of second-order Zermelo-Fraenkel set …

- The theory of infinite games, including infinite chess, Talk Math With Your Friends, June 2020
This will be accessible online talk about infinite chess and other infinite games for the Talk Math With Your Friends seminar, June 18, 2020 4 pm EST (9 pm UK). Zoom access information. Please come talk math with me! Abstract. I …

- Bi-interpretation of weak set theories, Oxford Set Theory Seminar, May 2020
This will be a talk for the newly founded Oxford Set Theory Seminar, May 20, 2020. Contact Sam Adam-Day (me@samadamday.com) for the Zoom access codes. Abstract: Set theory exhibits a truly robust mutual interpretability phenomenon: in any model of one …

- Philosophical Trials interview: Joel David Hamkins on Infinity, Gödel’s Theorems and Set Theory
I was interviewed by Theodor Nenu as the first installment of his Philosophical Trials interview series with philosophers, mathematicians and physicists. Theodor provided the following outline of the conversation: 00:00 Podcast Introduction 00:50 MathOverflow and books in progress …

- Bi-interpretation of weak set theories, Oberwolfach, April 2020
This will be a talk for the workshop in Set Theory at the Mathematisches Forschungsinstitute Oberwolfach, April 5-11, 2020. Note: the conference has been cancelled due to concerns over the Coronavirus-19. (Meanwhile, I have given the talk for the Oxford …

- Bi-interpretation in set theory, Bristol, February 2020
This will be a talk for the Logic and Set Theory seminar at the University of Bristol, on 25 February, 2020. Abstract: In contrast to the robust mutual interpretability phenomenon in set theory, Ali Enayat proved that bi-interpretation is absent: distinct …

- Philosophy meets maths, Oxford, January 2020
This will be a fun talk for the Philosophy Plus Science Taster Day, a fun day of events for prospective students in the joint philosophy degrees, whether Mathematics & Philosophy, Physics & Philosophy or Computer Science & Philosophy. The talk …

- Modal model theory, STUK 4, Oxford, December 2019
This will be my talk for the Set Theory in the United Kingdom 4, a conference to be held in Oxford on 14 December 2019. I am organizing the conference with Sam Adam-Day. Modal model theory Abstract. I shall introduce …

- I know that you know that I know that you know…. Oxford, October 2019
This will be a fun start-of-term Philosophy Undergraduate Welcome Lecture for philosophy students at Oxford in the Mathematics & Philosophy, Physics & Philosophy, Computer Science & Philosophy, and Philosophy & Linguistics degrees. New students are especially encouraged, but everyone is …

- Alan Turing’s theory of computation, Oxford and Cambridge Club, June 2019
I shall speak for the Oxford and Cambridge Club, in a joint event hosted by Maths and Science Group and the Military History Group, an evening (6 June 2019) with dinner and talks on the theme of the Enigma and …

- Computational self-reference and the universal algorithm, Queen Mary University of London, June 2019
This will be a talk for the Theory Seminar for the theory research group in Theoretical Computer Science at Queen Mary University of London. The talk will be held 4 June 2019 1:00 pm, ITL first floor. Abstract. Curious, often …

- The modal logic of potentialism, ILLC Amsterdam, May 2019
This will be a talk at the Institute of Logic, Language and Computation (ILLC) at the University of Amsterdam for events May 11-12, 2019. See Joel David Hamkins in Amsterdam 2019. Abstract: Potentialism can be seen as a fundamentally model-theoretic …

- Is there just one mathematical universe? DRIFT, Amsterdam, May 2019
This will be a talk for the Wijsgerig Festival DRIFT 2019, held in Amsterdam May 11, 2019. The theme of the conference is: Ontology. Abstract. What does it mean to make existence assertions in mathematics? Is there a mathematical universe, …

- Kelley-Morse set theory does not prove the class Fodor Principle, CUNY Set Theory Seminar, March, 2019
This will be talk for the CUNY Set Theory seminar, Friday, March 22, 2019, 10 am in room 6417 at the CUNY Graduate Center. Abstract. I shall discuss recent joint work with Victoria Gitman and Asaf Karagila, in which we …

- Must there be numbers we cannot describe or define? Definability in mathematics and the Math Tea argument, Norwich, February 2019
I shall speak for the Pure Mathematics Research Seminar at the University of East Anglia in Norwich on Monday, 25 February, 2019. Abstract. An old argument, heard perhaps at a good math tea, proceeds: “there must be some real numbers …

- Potentialism and implicit actualism in the foundations of mathematics, Jowett Society lecture, Oxford, February 2019
This will be a talk for the Jowett Society on 8 February, 2019. The talk will take place in the Oxford Faculty of Philosophy, 3:30 – 5:30pm, in the Lecture Room of the Radcliffe Humanities building. Abstract. Potentialism is the view, …

- Forcing as a computational process, Cambridge, Februrary 2019
This will be a talk for Set Theory in the United Kingdom (STUK 1), to be held in the other place, February 16, 2019. Abstract. We investigate the senses in which set-theoretic forcing can be seen as a computational process on …

- The rearrangement and subseries numbers: how much convergence suffices for absolute convergence? Mathematics Colloquium, University of Münster, January 2019
This will be a talk for the Mathematics Colloquium at the University of Münster, January 10, 2019. Abstract. The Riemann rearrangement theorem asserts that a series $\sum_n a_n$ is absolutely convergent if and only if every rearrangement $\sum_n a_{p(n)}$ of …

- An infinitary-logic-free proof of the Barwise end-extension theorem, with new applications, University of Münster, January 2019
This will be a talk for the Logic Oberseminar at the University of Münster, January 11, 2019. Abstract. I shall present a new proof, with new applications, of the amazing extension theorem of Barwise (1971), which shows that every countable …

- A new proof of the Barwise extension theorem, without infinitary logic, CUNY Logic Workshop, December 2018
I’ll be back in New York from Oxford, and this will be a talk for the CUNY Logic Workshop, December 14, 2018. Abstract. I shall present a new proof, with new applications, of the amazing extension theorem of Barwise (1971), …

- Faculty respondent to paper of Ethan Jerzak on Paradoxical Desires, Oxford Graduate Philosophy Conference, November 2018
The Oxford Graduate Philosophy Conference will be held at the Faculty of Philosophy November 10-11, 2018, with graduate students from all over the world speaking on their papers, with responses and commentary by Oxford faculty. I shall be the faculty respondent …

- On set-theoretic mereology as a foundation of mathematics, Oxford Phil Math seminar, October 2018
This will be a talk for the Philosophy of Mathematics Seminar in Oxford, October 29, 2018, 4:30-6:30 in the Ryle Room of the Philosopher Centre. Abstract. In light of the comparative success of membership-based set theory in the foundations of mathematics, …

- Parallels in universality between the universal algorithm and the universal finite set, Oxford Math Logic Seminar, October 2018
This will be a talk for the Logic Seminar in Oxford at the Mathematics Institute in the Andrew Wiles Building on October 9, 2018, at 4:00 pm, with tea at 3:30. Abstract. The universal algorithm is a Turing machine program $e$ that can …

- The rearrangement number: how many rearrangements of a series suffice to validate absolute convergence? Warwick Mathematics Colloquium, October 2018
This will be a talk for the Mathematics Colloquium at the University of Warwick, to be held October 19, 2018, 4:00 pm in Lecture Room B3.02 at the Mathematics Institute. I am given to understand that the talk will be …

- Plenary talk, 16th International Congress of Logic, Methodology and Philosophy of Science and Technology, CLMPST 2019, Prague
I shall be giving a keynote plenary talk for the 16th International Congress of Logic, Methodology and Philosophy of Science and Technology (CLMPST 2019), to be held 5-10 August 2019 at the Institute of Philosophy of the Czech Academy of Sciences in the …

- Set-theoretic potentialism and the universal finite set, Scandinavian Logic Symposium, June 2018
This will be an invited talk at the Scandinavian Logic Symposium SLS 2018, held at the University of Gothenburg in Sweden, June 11-13, 2018. Abstract. Providing a set-theoretic analogue of the universal algorithm, I shall define a certain finite set in set …

- The universal finite set, Rutgers Logic Seminar, April 2018
This will be a talk for the Rutgers Logic Seminar, April 2, 2018. Hill Center, Busch campus. Abstract. I shall define a certain finite set in set theory $$\{x\mid\varphi(x)\}$$ and prove that it exhibits a universal extension property: it can be …

- Determinacy for open class games is preserved by forcing, CUNY Set Theory Seminar, April 2018
This will be a talk for the CUNY Set Theory Seminar, April 27, 2018, GC Room 6417, 10-11:45am (please note corrected date). Abstract. Open class determinacy is the principle of second order set theory asserting of every two-player game of perfect …

- Nonamalgamation in the Cohen generic multiverse, CUNY Logic Workshop, March 2018
This will be a talk for the CUNY Logic Workshop on March 23, 2018, GC 6417 2-3:30pm. Abstract. Consider a countable model of set theory $M$ in the context of all its successive forcing extensions and grounds. This generic multiverse has …

- Modal principles of potentialism, Oxford, January 2018
This was a talk I gave at University College Oxford to the philosophy faculty. Abstract. One of my favorite situations occurs when philosophical ideas or issues inspire a bit of mathematical analysis, which in turn raises further philosophical questions and ideas, …

- On the strengths of the class forcing theorem and clopen class game determinacy, Prague set theory seminar, January 2018
This will be a talk for the Prague set theory seminar, January 24, 11:00 am to about 2pm (!). Abstract. The class forcing theorem is the assertion that every class forcing notion admits corresponding forcing relations. This assertion is not provable …

- Self reference in computability theory and the universal algorithm, Ouroboros: Formal Criteria of Self-Reference in Mathematics and Philosophy, Bonn, February 2018
This will be a talk for the conference: Ouroboros: Formal Criteria of Self-Reference in Mathematics and Philosophy, held in Bonn, February 16-18, 2018. Abstract. I shall give an elementary account of the universal algorithm, due to Woodin, showing how the capacity …

- The universal algorithm and the universal finite set, Prague 2018
This will be a talk at the Prague Gathering of Logicians & Beauty of Logic 2018, January 25-27, 2018. Abstract. The universal algorithm is a Turing machine program $e$ that can in principle enumerate any finite sequence of numbers, if run in …

- Set-theoretic potentialism, Winter School in Abstract Analysis 2018, Hejnice, Czech Republic
This will be a tutorial lecture series for the Winter School in Abstract Analysis 2018, held in Hejnice of the Czech Republic. Abstract. I shall introduce and develop the theory of set-theoretic potentialism. A potentialist system is a collection of first-order …

- A universal finite set, CUNY Logic Workshop, November 2017
This will be a talk for the CUNY Logic Workshop, November 17, 2017, 2pm GC Room 6417. Abstract. I shall define a certain finite set in set theory $$\{x\mid\varphi(x)\}$$ and prove that it exhibits a universal extension property: it can be …

- The hierarchy of second-order set theories between GBC and KM and beyond
This was a talk at the upcoming International Workshop in Set Theory at the Centre International de Rencontres Mathématiques at the Luminy campus in Marseille, France, October 9-13, 2017. Abstract. Recent work has clarified how various natural second-order set-theoretic principles, such …

- Arithmetic potentialism and the universal algorithm, CUNY Logic Workshop, September 2017
This will be a talk for the CUNY Logic Workshop at the CUNY Graduate Center, September 8, 2017, 2-3:30, room GC 6417. Abstract. Consider the collection of all the models of arithmetic under the end-extension relation, which forms a potentialist system …

- The modal principles of potentialism in mathematics, Logic and Metaphysics Workshop, CUNY, November 2017
This will be a talk on November 6, 2017 for the Logic and Metaphysics workshop at the CUNY Graduate Center, run by Graham Priest. Room GC 3209. The modal principles of potentialism in mathematics Abstract. Potentialism is the view in the …

- The inner-model and ground-model reflection principles, CUNY Set Theory seminar, September 2017
This will be a talk for the CUNY Set Theory seminar on September 1, 2017, 10 am. GC 6417. Abstract. The inner model reflection principle asserts that whenever a statement $\varphi(a)$ in the first-order language of set theory is true in the …

- All countable models of set theory have the same inclusion relation up to isomorphism, CUNY Logic Workshop, April 2017
This will be a talk for the CUNY Logic Workshop, April 28, 2:00-3:30 in room 6417 at the CUNY Graduate Center. Abstract. Take any countable model of set theory $\langle M,\in^M\rangle\models\text{ZFC}$, whether well-founded or not, and consider the corresponding inclusion …

- Open and clopen determinacy for proper class games, VCU MAMLS April 2017
This will be a talk for the Mid-Atlantic Mathematical Logic Seminar at Virginia Commonwealth University, a conference to be held April 1-2, 2017. Abstract. The principle of open determinacy for class games — two-player games of perfect information with plays …

- Computable quotient presentations of models of arithmetic and set theory, CUNY set theory seminar, March 2017
This will be a talk for the CUNY Set Theory Seminar on March 10, 2017, 10:00 am in room 6417 at the CUNY Graduate Center. Abstract. I shall prove various extensions of the Tennenbaum phenomenon to the case of computable …

- Set-theoretic geology and the downward directed grounds hypothesis, Bonn, January 2017
This will be a talk for the University of Bonn Logic Seminar, Friday, January 13, 2017, at the Hausdorff Center for Mathematics. Abstract. Set-theoretic geology is the study of the set-theoretic universe $V$ in the context of all its ground models …

- Transfinite game values in infinite chess, including new progress, Bonn, January 2017
This will be a talk January 10, 2017 for the Basic Notions Seminar, aimed at students, post-docs, faculty and guests of the Mathematics Institute, University of Bonn. Abstract. I shall give a …

- Recent advances in set-theoretic geology, Harvard Logic Colloquium, October 2016
I will speak at the Harvard Logic Colloquium, October 20, 2016, 4-6 pm. Abstract. Set-theoretic geology is the study of the set-theoretic universe $V$ in the context of all its ground models and those of its forcing extensions. For example, …

- Set-theoretic potentialism, CUNY Logic Workshop, September, 2016
This will be a talk for the CUNY Logic Workshop, September 16, 2016, at the CUNY Graduate Center, Room 6417, 2-3:30 pm. Abstract. In analogy with the ancient views on potential as opposed to actual infinity, set-theoretic potentialism is the philosophical …

- Set-theoretic mereology as a foundation of mathematics, Logic and Metaphysics Workshop, CUNY, October 2016
This will be a talk for the Logic and Metaphysics Workshop at the CUNY Graduate Center, GC 5382, Monday, October 24, 2016, 4:15-6:15 pm. Abstract. In light of the comparative success of membership-based set theory in the foundations of mathematics, since …

- The modal logic of set-theoretic potentialism, Kyoto, September 2016
This will be a talk for the workshop conference Mathematical Logic and Its Applications, which will be held at the Research Institute for Mathematical Sciences, Kyoto University, Japan, September 26-29, 2016, organized by Makoto Kikuchi. The workshop is being held …

- The rearrangement number: how many rearrangements of a series suffice to verify absolute convergence? Mathematics Colloquium at Penn, September 2016
This will be a talk for the Mathematics Colloquium at the University of Pennsylvania, Wednesday, September 14, 2016, 3:30 pm, tea at 3 pm, in the mathematics department. Abstract. The well-known Riemann rearrangement theorem asserts that a series $\sum_n a_n$ …

- Set-theoretic geology and the downward-directed grounds hypothesis, CUNY Set Theory seminar, September 2016
This will be a talk for the CUNY Set Theory Seminar, September 2 and 9, 2016. In two talks, I shall give a complete detailed account of Toshimichi Usuba’s recent proof of the strong downward-directed grounds hypothesis. This breakthrough result …

- Pluralism-inspired mathematics, including a recent breakthrough in set-theoretic geology, Set-theoretic Pluralism Symposium, Aberdeen, July 2016
Set-theoretic Pluralism, Symposium I, July 12-17, 2016, at the University of Aberdeen. My talk will be the final talk of the conference. Abstract. I shall discuss several bits of pluralism-inspired mathematics, including especially an account of Toshimichi Usuba’s recent proof of …

- Same structure, different truths, Stanford University CSLI, May 2016
This will be a talk for the Workshop on Logic, Rationality, and Intelligent Interaction at the CSLI, Stanford University, May 27-28, 2016. Abstract. To what extent does a structure determine its theory of truth? I shall discuss several surprising mathematical …

- Open determinacy for games on the ordinals, Torino, March 2016
This will be a seminar talk I shall give on March 3, 2016 at the University of Torino, Italy, in the same department where Giuseppe Peano had his position. I shall be in Italy for the dissertation …

- Freiling’s axiom of symmetry, or throwing darts at the real line, Graduate Student Colloquium, April 2016
This will be a talk I’ll give at the CUNY Graduate Center Graduate Student Colloquium on Monday, April 11 (new date!), 2016, 4-4:45 pm. The talk will be aimed at a general audience of mathematics graduate students. Abstract. I shall give …

- The rearrangement number: how many rearrangements of a series suffice to verify absolute convergence? Vassar Math Colloquium, November 2015
This will be a talk for the Mathematics Colloquium at Vassar College, November 10, 2015, tea at 4:00 pm, talk at 4:15 pm, Rockefeller Hall 310 Abstract. The Riemann rearrangement theorem asserts that a series $\sum_n a_n$ is absolutely convergent …

- The rearrangement number, CUNY set theory seminar, November 2015
This will be a talk for the CUNY Set Theory Seminar on November 6, 2015. The Riemann rearrangement theorem states that a convergent real series $\sum_n a_n$ is absolutely convergent if and only if the value of the sum is …

- Open determinacy for games on the ordinals is stronger than ZFC, CUNY Logic Workshop, October 2015
This will be a talk for the CUNY Logic Workshop on October 2, 2015. Abstract. The principle of open determinacy for class games — two-player games of perfect information with plays of length $\omega$, where the moves are chosen from a …

- Upward closure in the generic multiverse of a countable model of set theory, RIMS 2015, Kyoto, Japan
This will be a talk for the conference Recent Developments in Axiomatic Set Theory at the Research Institute for Mathematical Sciences (RIMS) in Kyoto, Japan, September 16-18, 2015. Abstract. Consider a countable model of set theory amongst its forcing extensions, the ground …

- Universality and embeddability amongst the models of set theory, CTFM 2015, Tokyo, Japan
This will be a talk for the Computability Theory and Foundations of Mathematics conference at the Tokyo Institute of Technology, September 7-11, 2015. The conference is held in celebration of Professor Kazuyuki Tanaka’s 60th birthday. Abstract. Recent results on the embeddability …

- The hypnagogic digraph, with applications to embeddings of the set-theoretic universe, JMM Special Session on Surreal Numbers, Seattle, January 2016
This will be an invited talk for the AMS-ASL special session on Surreal Numbers at the 2016 Joint Mathematics Meetings in Seattle, Washington, January 6-9, 2016. Abstract. The hypnagogic digraph, a proper-class analogue of the countable random $\mathbb{Q}$-graded digraph, is a surreal-numbers-graded acyclic …

- The absolute truth about non-absolute truth, JAF – Weak Arithmetics Days, New York, July 2015
This will be a talk for the Journées sur les Arithmétiques Faibles – Weak Arithmetics Days conference, held in New York at the CUNY Graduate Center, July 7 – 9, 2015. Abstract. I will discuss several fun theorems and folklore results illustrating …

- The weakly compact embedding property, Apter-Gitik celebration, CMU 2015
This will be a talk at the Conference in honor of Arthur W. Apter and Moti Gitik at Carnegie Mellon University, May 30-31, 2015. I am pleased to be a part of this conference in honor of the 60th birthdays …

- The continuum hypothesis and other set-theoretic ideas for non-set-theorists, CUNY Einstein Chair Seminar, April, 2015
At Dennis Sullivan’s request, I shall speak on set-theoretic topics, particularly the continuum hypothesis, for the Einstein Chair Mathematics Seminar at the CUNY Graduate Center, April 27, 2015, in two parts: An introductory background talk at 11 am, Room GC 6417 The …

- I know that you know that I know that you know…., CSI Undergraduate Conference on Research, Scholarship, and Performance, April 2015
I shall give the plenary talk at the CSI Undergraduate Conference on Research, Scholarship, and Performance, April 30, 2015. My presentation will be followed by a musical performance. This is a conference where undergraduate students show off their various scholarly …

- Embeddings of the universe into the constructible universe, current state of knowledge, CUNY Set Theory Seminar, March 2015
This will be a talk for the CUNY Set Theory Seminar, March 6, 2015. I shall describe the current state of knowledge concerning the question of whether there can be an embedding of the set-theoretic universe into the constructible universe. …

- An introduction to the theory of infinite games, with examples from infinite chess, University of Connecticut, December 2014
This will be a talk for the interdisciplinary Group in Philosophical and Mathematical Logic at the University of Connecticut in Storrs, on December 5, 2014. Abstract. I shall give a general introduction to the theory of infinite games, with a focus …

- Does definiteness-of-truth follow from definiteness-of-objects? NY Philosophical Logic Group, NYU, November 2014
This will be a talk for the New York Philosophical Logic Group, November 10, 2014, 5-7pm, at the NYU Philosophy Department, 5 Washington Place, Room 302. Abstract. This talk — a mix of mathematics and philosophy — concerns the extent …

- When does every definable set have a definable member? CUNY Set Theory Seminar, October 2014
This will be a talk for the CUNY set theory seminar, October 10, 2014, 12pm GC 6417. Abstract. Although the concept of `being definable’ is not generally expressible in the language of set theory, it turns out that the models …

- The theory of infinite games: how to play infinite chess and win, VCU Math Colloquium, November 2014
I shall speak at the Virginia Commonwealth University Math Colloquium on November 21, 2014. Abstract. I shall give a general introduction to the theory of infinite games, using infinite chess—chess played on an infinite chessboard stretching without bound in every direction—as …

- The span of infinity, roundtable discussion at The Helix Center, October 2014
I was a panelist at The Span of Infinity, a roundtable discussion held at The Helix Center, at the New York Psychoanalytic Society & Institute, 247 E 82nd Street, on October 25, 2014, 2:30 – 4:30 pm. The Helix Center describes …

- The pluralist perspective on the axiom of constructibility, MidWest PhilMath Workshop, Notre Dame, October 2014
This will be a featured talk at the Midwest PhilMath Workshop 15, held at Notre Dame University October 18-19, 2014. W. Hugh Woodin and I will each give one-hour talks in a session on Perspectives on the foundations of set …

- Large cardinals need not be large in HOD, International Workshop on Set Theory, CIRM, Luminy, September 2014
I shall speak at the 13th International Workshop on Set Theory, held at the CIRM Centre International de Rencontres Mathématiques in Luminy near Marseille, France, September 29 to October 3, 2014. Abstract. I shall prove that large cardinals need not generally exhibit their large cardinal …

- A meeting at the crossroads – science, performance and the art of possibility, panel discussion, Underground Zero Festival, Intrinsic Value Project, July 2014
I shall be a panelist at A meeting at the crossroads – science, performance and the art of possibility, a panel discussion considering the intrinsic value of Art and Science, a part of the Intrinsic Value series at the Undergroundzero Festival 2014. Are …

- Higher infinity and the foundations of mathematics, plenary General Public Lecture, AAAS, June, 2014
I have been invited to give a plenary General Public Lecture at the 95th annual meeting of the American Association for the Advancement of Science (Pacific Division), which will be held in Riverside, California, June 17-20, 2014. The talk is sponsored …

- Boldface resurrection and the strongly uplifting cardinals, the superstrongly unfoldable cardinals and the almost-hugely unfoldable cardinals, BEST 2014
I will speak at the BEST conference, which is held as a symposium in the much larger 95th Annual Meeting of the American Association for the Advancement of Science, at the University of California at Riverside, June 18-20, 2014. This talk will be for …

- Tutorial on Boolean ultrapowers, BLAST 2015, Las Cruces, NM
I shall give a tutorial lecture series on Boolean ultrapowers, two or three lectures, at the BLAST conference in Las Cruces, New Mexico, January 5-9, 2015. (The big AMS meeting in San Antonio, reportedly a quick flight, begins on the 10th.) …

- A natural strengthening of Kelley-Morse set theory, CUNY Logic Workshop, May 2014
This will be a talk for the CUNY Logic Workshop on May 2, 2014. Abstract. I shall introduce a natural strengthening of Kelley-Morse set theory KM to the theory we denote KM+, by including a certain class collection principle, which holds in …

- Transfinite game values in infinite chess and other infinite games, Hausdorff Center, Bonn, May 2014
I shall be very pleased to speak at the colloquium and workshop Infinity, computability, and metamathematics, celebrating the 60th birthdays of Peter Koepke and Philip Welch, held at the Hausdorff Center for Mathematics May 23-25, 2014 at the Universität Bonn. My …

- Large cardinals need not be large in HOD, Rutgers logic seminar, April 2014
I shall speak at the Rutgers Logic Seminar on April 21, 2014, 5:00-6:20 pm, Room 705, Hill Center, Busch Campus, Rutgers University. Abstract. I will show that large cardinals, such as measurable, strong and supercompact cardinals, need not exhibit their large cardinal …

- Large cardinals need not be large in HOD, CUNY Set Theory Seminar, January 2014
This will be a talk for the CUNY Set Theory Seminar, January 31, 2014, 10:00 am. Abstract. I will demonstrate that a large cardinal need not exhibit its large cardinal nature in HOD. I will begin with the example of a …

- Superstrong and other large cardinals are never Laver indestructible, ASL 2014, Boulder, May 2014
This will be an invited talk at the ASL 2014 North American Annual Meeting (May 19-22, 2014) in the special session Set Theory in Honor of Rich Laver, organized by Bill Mitchell and Jean Larson. Abstract. The large cardinal indestructibility phenomenon, discovered …

- Universal structures, GC MathFest, February 2014
This will be a talk for the CUNY Graduate Center MathFest, held on the afternoon of Februrary 4, 2014, intended for graduate-school-bound undergraduate students, including prospective students for the CUNY Graduate Center, giving them a chance to meet graduate students …

- Satisfaction is not absolute, Dartmouth Logic Seminar, January 2014
This will be a talk for the Dartmouth Logic Seminar on January 23rd, 2014. Abstract. I will discuss a number of theorems showing that the satisfaction relation of first-order logic is less absolute than might have been supposed. Two models …

- Infinite chess and the theory of infinite games, Dartmouth Mathematics Colloquium, January 2014
This will be a talk for the Dartmouth Mathematics Colloquium on January 23rd, 2014. Abstract. Using infinite chess as a central example—chess played on an infinite edgeless board—I shall give a general introduction to the theory of infinite games. Infinite chess …

- Rubik's cube competition, CSI, November 14, 2013
Come and compete in the CSI Rubik’s cube competition! November 14, 2013, College of Staten Island of CUNY, 1S-107, 2:30 pm. Sponsored by MTH 339, and the CSI Math Club. As a part of the undergraduate course in abstract algebra (MTH …

- Win the game of Nim! CSI Math Club, October, 2013
This will be a talk for the CSI Math Club on October 31, 2013 at 2:30 pm in room 1S-107. Abstract Come and learn how to play and win the game of Nim! The game has two players, faced with …

- Address at the Dean's List Ceremony
As the designated faculty speaker, selected after nominations from all the various departments at the college, I made the following remarks, in full academic regalia, at the Dean’s List ceremony this evening at the College of Staten Island. Thank you …

- Satisfaction is not absolute, CUNY Logic Workshop, September 2013
This will be a talk for the CUNY Logic Workshop on September 27, 2013. Abstract. I will discuss a number of theorems showing that the satisfaction relation of first-order logic is less absolute than might have been supposed. Two models …

- The role of the axiom of foundation in the Kunen inconsistency, CUNY September 2013
This will be a talk for the CUNY Set Theory Seminar on September 20, 2013 (date tentative). Abstract. The axiom of foundation plays an interesting role in the Kunen inconsistency, the assertion that there is no nontrivial elementary embedding of the …

- Exploring the Frontiers of Incompleteness, Harvard, August 2013
I will be participating in the culminating workshop of the Exploring the Frontiers of Incompleteness conference series at Harvard University, to take place August 31-September 1, 2013. Rather than conference talks, the program will consist of extended discussion sessions by …

- Satisfaction is not absolute, Connecticut, October 2013
This will be a talk for the Logic Seminar in the Mathematics Department at the University of Connecticut in Storrs on October 25, 2013. Abstract. The satisfaction relation $\mathcal{N}\models\varphi[\vec a]$ of first-order logic, it turns out, is less absolute than might …

- Workshop on paraconsistent set theory, Connecticut, October 2013
I’ll be participating in a workshop at the University of Connecticut, Storrs, philosophy department on October 26-27, 2013, on paraconsistent set theory, organized by Graham Priest and JC Beall. I am given to understand that part of the goal is …

- Universal structures: the countable random graph, the surreal numbers and the hypnagogic digraph, Swarthmore College, October 2013
I’ll be speaking for the Swarthmore College Mathematics and Statistics Colloquium on October 8th, 2013. Abstract. I’ll be giving an introduction to universal structures in mathematics, where a structure $\mathcal{M}$ is universal for a class of …

- Embeddability amongst the countable models of set theory, plenary talk for ASL / Joint Math Meetings in Baltimore, January 2014
A one-hour plenary talk for the ASL at the Joint Math Meetings, January 15-18, 2014 in Baltimore, MD. Saturday January 18, 2014, 2:00 p.m.-2:50 p.m, Room 319 BCC Abstract. A surprisingly vigorous embeddability phenomenon has recently been uncovered amongst the countable models …

- Panelist at the Infinity Salon for the World Science Festival, NYC, June 2013
The World Science Festival is coming to New York (May 29 — June 2), with numerous interesting events, including the infinity salon, an intimate, free-wheeling discussion about infinity, entitled The future of Infinity: Solving Math’s most notorious problem, for an audience of experts. I shall …

- A multiverse perspective in mathematics and set theory: does every mathematical statement have a definite truth value? Shanghai, June 2013
This will be a talk for specialists in philosophy, mathematics and the philosophy of mathematics, given as part of the workshop Metamathematics and Metaphysics, June 15, 2013, sponsored by the group in Mathematical Logic at Fudan University. Abstract: Much of the debate …

- Universality, saturation and the surreal number line, Shanghai, June 2013
This will be a short lecture series given at the conclusion of the graduate logic class in the Mathematical Logic group at Fudan University in Shanghai, June 13, 18 (or 20), 2013. I will present an elementary introduction to the theory of universal …

- Playful paradox with large numbers, infinity and logic, Shanghai, June 2013
This will be a talk at Fudan University in Shanghai, China, June 12, 2013, sponsored by the group in Mathematical Logic at Fudan, for a large audience of students. Abstract: For success in mathematics and science, I recommend an attitude of playful …

- Algebraicity and implicit definability in set theory, CUNY, May 2013
This is a talk May 10, 2013 for the CUNY Set Theory Seminar. Abstract. An element a is definable in a model M if it is the unique object in M satisfying some first-order property. It is algebraic, in contrast, …

- The theory of infinite games, with examples, including infinite chess
This will be a talk on April 30, 2013 for a joint meeting of the Yeshiva University Mathematics Club and the Yeshiva University Philosophy Club. The event will take place in 5:45 pm in Furst Hall, on the corner of Amsterdam …

- Pluralism in mathematics: the multiverse view in set theory and the question of whether every mathematical statement has a definite truth value, Rutgers, March 2013
This is a talk for the Rutgers Logic Seminar on March 25th, 2013. Simon Thomas specifically requested that I give a talk aimed at philosophers. Abstract. I shall describe the debate on pluralism in the philosophy of set theory, specifically on …

- The omega one of chess, CUNY, March, 2013
This is a talk for the New York Set Theory Seminar on March 1, 2013. This talk will be based on my recent paper with C. D. A. Evans, Transfinite game values in infinite chess. Infinite chess is chess played on …

- On the axiom of constructibility and Maddy’s conception of restrictive theories, Logic Workshop, February 2013
This is a talk for the CUNY Logic Workshop on February 15, 2013. This talk will be based on my paper, A multiverse perspective on the axiom of constructibility. Set-theorists often argue against the axiom of constructibility $V=L$ on the grounds that …

- Superstrong cardinals are never Laver indestructible, and neither are extendible, almost huge and rank-into-rank cardinals, CUNY, January 2013
This is a talk for the CUNY Set Theory Seminar on February 1, 2013, 10:00 am. Abstract. Although the large cardinal indestructibility phenomenon, initiated with Laver’s seminal 1978 result that any supercompact cardinal $\kappa$ can be made indestructible by $\lt\kappa$-directed closed …

- Pluralism in set theory: does every mathematical statement have a definite truth value? GC Philosophy Colloquium, 2012
This will be my talk for the CUNY Graduate Center Philosophy Colloquium on November 28, 2012. I will be speaking on topics from some of my recent articles: The set-theoretic multiverse The multiverse perspective on the axiom of constructibility Is the …

- The countable models of set theory are linearly pre-ordered by embeddability, Rutgers, November 2012
This will be a talk for the Rutgers Logic Seminar on November 19, 2012. Abstract. I will speak on my recent theorem that every countable model of set theory $M$, including every well-founded model, is isomorphic to a submodel of its …

- Every countable model of set theory is isomorphic to a submodel of its own constructible universe, Barcelona, December, 2012
This will be a talk for a set theory workshop at the University of Barcelona on December 15, 2012, organized by Joan Bagaria. Abstract. Every countable model of set theory $M$, including every well-founded model, is isomorphic to a submodel of …

- 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 …

- The least weakly compact cardinal can be unfoldable, weakly measurable and nearly $\theta$-supercompact, New York, September 14, 2012
This will be a talk for the CUNY Set Theory seminar on September 14, 2012. Abstract. Starting from suitable large cardinal hypothesis, I will explain how to force the least weakly compact cardinal to be unfoldable, weakly measurable and, indeed, …

- Recent progress on the modal logic of forcing and grounds, CUNY Logic Workshop, September 2012
This will be a talk for the CUNY Logic Workshop on September 7, 2012. Abstract. The modal logic of forcing arises when one considers a model of set theory in the context of all its forcing extensions, with “true in …

- Every countable model of set theory embeds into its own constructible universe, Fields Institute, Toronto, August 2012
This will be a talk for the Toronto set theory seminar at the Fields Institute, University of Toronto, on August 24, 2012. Abstract. Every countable model of set theory $M$, including every well-founded model, is isomorphic to a submodel of its own constructible universe. …

- The mate-in-n problem of infinite chess is decidable, Cambridge, June 2012
This will be a contributed talk at the Turing Centenary Conference CiE 2012 held June 18-23, 2012 in Cambridge, UK. Abstract. The mate-in-$n$ problem of infinite chess—chess played on an infinite edgeless board—is the problem of determining whether a designated player can …

- The hierarchy of equivalence relations on the natural numbers under computable reducibility, Chicheley Hall, June 2012
This will be a talk at The Incomputable, a workshop held June 12-15, 2012 at the Kavli Royal Society International Centre at Chicheley Hall as a part of the program Semantics and Syntax: A Legacy of Alan Turing organized by the …

- The countable models of ZFC, up to isomorphism, are linearly pre-ordered by the submodel relation; indeed, every countable model of ZFC, including every transitive model, is isomorphic to a submodel of its own $L$, New York, 2012
This will be a talk on May 18, 2012 for the CUNY Logic Workshop on some extremely new work. The proof uses finitary digraph combinatorics, including the countable random digraph and higher analogues involving uncountable Fraisse limits, the surreal numbers …

- The omega one of infinite chess, New York, 2012
This will be a talk on May 18, 2012 for the CUNY Set Theory Seminar. Infinite chess is chess played on an infinite edgeless chessboard. The familiar chess pieces move about according to their usual chess rules, and each player strives …

- Must there be numbers we cannot describe or define? Pointwise definability and the Math Tea argument, Bristol, April 2012
This is a talk I plan to give to the set theory seminar at the University of Bristol on April 18, 2012. An old argument, heard at a good math tea, proceeds: “there must be some real numbers that we can neither …

- Fun and paradox with large numbers, logic and infinity, Philadelphia 2012
This is a fun talk I will give at Temple University for the mathematics undergraduates in the Senior Problem Solving forum. We’ll be exploring some of the best puzzles and paradoxes I know of that arise with large numbers and …

- What happens when one iteratively computes the automorphism group of a group? Temple University, Philadelphia 2012
This is a talk I shall give for the Mathematics Colloquium at Temple University, April 23, 2012. The automorphism tower of a group is obtained by computing its automorphism group, the automorphism group of that group, and so on, iterating transfinitely. The question, …

- The automorphism tower problem for groups, Bristol 2012
Isaac Newton 20th Anniversary Lecture. This is a talk I shall give at the University of Bristol, School of Mathematics, April 17, 2012, at the invitation of Philip Welch. The automorphism tower of a group is obtained by computing its automorphism group, the …

- The hierarchy of equivalence relations on the natural numbers under computable reducibility, Cambridge, March 2012
This is a talk I shall give at the workshop on Logical Approaches to Barriers in Complexity II, March 26-30, 2012, a part of the program Semantics and Syntax: A Legacy of Alan Turing at the Isaac Newton Institute for Mathematical …

- Infinite chess: the mate-in-n problem is decidable and the omega-one of chess, Cambridge, March 2012
I have just taken up a visiting fellow position at the Isaac Newton Institute for mathematical sciences in Cambridge, UK, where I am participating in the program Syntax and Semantics: the legacy of Alan Turing. I was asked to give a brief introduction …

- The hierarchy of equivalence relations on $\mathbb{N}$ under computable reducibility, New York March 2012
I gave a talk at the CUNY MAMLS conference March 9-10, 2012 at the City University of New York. This talk will be about a generalization of the concept of Turing degrees to the hierarchy of equivalence relations on $\mathbb{N}$ under computable …

- Panel discussion on the unity and diversity of logic, New York, March 2012
As a part of the Spring 2012 Mid-Atlanatic Mathematical Logic Seminar, to be held March 9-10, 2012 at the CUNY Graduate Center, I shall participate in the following panel discussion. Panel discussion: The unity and diversity of logic Abstract. The field of …

- The hierarchy of equivalence relations on $\mathbb{N}$ under computable reducibility, Florida, 2012
This is a talk at the Alan Turing centenary conference at Florida Atlantic University, January 13-15, 2012, sponsored by MAMLS, and part of the 2012 Alan Turing Year of events in celebration of the one hundredth year of the birth of …

- Set theory: universe or multiverse? Vienna, 2011
This talk was held as part of the Logic Cafe series at the Institute of Philosophy at the University of Vienna, October 31, 2011. A traditional Platonist view in set theory, what I call the universe view, holds that there is …

- Must there be non-definable numbers? Pointwise definability and the math-tea argument, KGRC, Vienna 2011
This talk will be a part of the “Advanced Introduction” series for graduate students at the the Kurt Gödel Research Center, November 4, 2011. An old argument, heard perhaps at math tea, proceeds: “there must be some real numbers that we …

- Generalizations of the Kunen inconsistency, KGRC, Vienna 2011
This is a talk at the research seminar of the Kurt Gödel Research Center, November 3, 2011. I shall present several generalizations of the well-known Kunen inconsistency that there is no nontrivial elementary embedding from the set-theoretic universe V to itself, …

- The set-theoretical multiverse: a natural context for set theory, Japan 2009
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- The Ground Axiom
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- The multiverse perspective on determinateness in set theory, Harvard, 2011
This talk, taking place October 19, 2011, is part of the year-long Exploring the Frontiers of Incompleteness (EFI) series at Harvard University, a workshop focused on the question of determinateness in set theory, a central question in the philosophy of set theory. …

- The multiverse view in set theory, Singapore 2011
A talk at the Asian Initive for Infinity: Workshop on Infinity and Truth, July 25-29, 2011, National University of Singapore. I shall outline and defend the Multiverse view in set theory, the view that there are many set-theoretic universes, each instantiating …

- Generalizations of the Kunen Inconsistency, Singapore 2011
A talk at the Prospects of Infinity: Workshop on Set Theory at the National University of Singapore, July 18-22, 2011. I shall present several generalizations of the well-known Kunen inconsistency that there is no nontrivial elementary embedding from the set-theoretic universe V …

- The modal logic of forcing, London 2011
A talk at the conference on Set Theory and Higher-Order Logic: Foundational Issues and Mathematical Developments, following the summer school, at the University of London, Birkbeck, July 1-6, 2011. What are the most general principles relating forceability and truth? As …

- A tutorial in set-theoretic geology, London 2011
A three-lecture mini-course tutorial in set-theoretic geology at the summer school Set Theory and Higher-Order Logic: Foundational Issues and Mathematical Developments, August 1-6, 2011, University of London, Birkbeck. The technique of forcing in set theory is customarily thought of as …

- What is the theory of ZFC-Powerset? Toronto 2011
This was a talk at the Toronto Set Theory Seminar held April 22, 2011 at the Fields Institute in Toronto. The theory ZFC-, consisting of the usual axioms of ZFC but with the powerset axiom removed, when axiomatized by extensionality, foundation, …

- An introduction to Boolean ultrapowers, Bonn, 2011
A four-lecture tutorial on the topic of Boolean ultrapowers at the Young Set Theory Workshop at the Hausdorff Center for Mathematics in Königswinter near Bonn, Germany, March 21-25, 2011. Boolean ultrapowers generalize the classical ultrapower construction on a power-set algebra to the …

- Pointwise definable models of set theory, extended abstract, Oberwolfach 2011
[bibtex key=Hamkins2011:PointwiseDefinableModelsOfSetTheoryExtendedAbstract]

- The set-theoretic multiverse: a model-theoretic philosophy of set theory, Paris, 2010
A talk at the Philosophy and Model Theory conference held June 2-5, 2010 at the Université Paris Ouest Nanterre. Set theorists commonly regard set theory as an ontological foundation for the rest of mathematics, in the sense that other abstract mathematical objects can be construed …