nylogic profile | set theory talks profile

- June 21, 2024:
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 … Continue reading
- June 19, 2024:
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 … Continue reading
- May 17, 2024:
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 … Continue reading
- May 17, 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.
- March 15, 2024:
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 … Continue reading
- March 11, 2024:
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 … Continue reading
- March 1, 2024:
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 … Continue reading
- February 12, 2024:
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 … Continue reading
- February 6, 2024:
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 … Continue reading
- January 16, 2024:
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 … Continue reading
- December 4, 2023:
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 … Continue reading
- November 17, 2023:
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 $\Delta\subseteq\omega^\omega$, … Continue reading
- October 18, 2023:
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 … Continue reading
- September 28, 2023:
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 … Continue reading
- September 21, 2023:
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 … Continue reading
- August 13, 2023:
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 … Continue reading
- June 17, 2023:
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 … Continue reading
- May 22, 2023:
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 … Continue reading
- May 18, 2023:
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 … Continue reading
- May 5, 2023:
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 … Continue reading
- May 2, 2023:
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 … Continue reading
- April 25, 2023:
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 … Continue reading
- April 4, 2023:
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 … Continue reading
- March 16, 2023:
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 … Continue reading
- March 15, 2023:
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 … Continue reading
- January 31, 2023:
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, … Continue reading
- January 9, 2023:
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 … Continue reading
- November 22, 2022:
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 … Continue reading
- October 11, 2022:
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 … Continue reading
- September 29, 2022:
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 … Continue reading
- September 28, 2022:
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 … Continue reading
- September 21, 2022:
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 … Continue reading
- September 12, 2022:
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 … Continue reading
- September 8, 2022:
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 … Continue reading
- August 29, 2022:
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 … Continue reading
- June 18, 2022:
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? … Continue reading
- May 27, 2022:
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 … Continue reading
- April 15, 2022:
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 … Continue reading
- February 12, 2022:
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 … Continue reading
- February 8, 2022:
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 … Continue reading
- January 10, 2022:
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 … Continue reading
- December 8, 2021:
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.
- December 4, 2021:
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 … Continue reading
- November 11, 2021:
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 … Continue reading
- November 1, 2021:
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 … Continue reading
- September 15, 2021:
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 … Continue reading
- August 23, 2021:
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 … Continue reading
- July 19, 2021:
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 … Continue reading
- April 14, 2021:
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 … Continue reading
- March 26, 2021:
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 … Continue reading
- March 19, 2021:
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 … Continue reading
- March 9, 2021:
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 … Continue reading
- January 25, 2021:
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 … Continue reading
- January 22, 2021:
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 … Continue reading
- November 18, 2020:
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 … Continue reading
- November 14, 2020:
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 … Continue reading
- October 28, 2020:
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 … Continue reading
- September 21, 2020:
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 … Continue reading
- June 26, 2020:
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 … Continue reading
- June 18, 2020:
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 … Continue reading
- May 20, 2020:
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 … Continue reading
- April 11, 2020:
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 … Continue reading
- April 1, 2020:
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 … Continue reading
- February 25, 2020:
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 … Continue reading
- January 10, 2020:
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 … Continue reading
- December 14, 2019:
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 … Continue reading
- October 16, 2019:
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 … Continue reading
- August 5, 2019:
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 … Continue reading
- June 6, 2019:
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 … Continue reading
- June 4, 2019:
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 … Continue reading
- May 11, 2019:
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, … Continue reading
- May 11, 2019:
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 … Continue reading
- March 22, 2019:
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 … Continue reading
- February 16, 2019:
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 … Continue reading
- February 8, 2019:
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, … Continue reading
- January 11, 2019:
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 … Continue reading
- December 15, 2018:
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), … Continue reading
- November 10, 2018:
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 … Continue reading
- October 29, 2018:
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, … Continue reading
- October 19, 2018:
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 … Continue reading
- October 9, 2018:
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 … Continue reading
- June 11, 2018:
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 … Continue reading
- April 23, 2018:
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 … Continue reading
- April 2, 2018:
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 … Continue reading
- March 23, 2018:
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 … Continue reading
- February 16, 2018:
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 … Continue reading
- January 29, 2018:
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, … Continue reading
- January 27, 2018:
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 … Continue reading
- January 25, 2018:
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 … Continue reading
- January 24, 2018:
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 … Continue reading
- November 17, 2017:
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 … Continue reading
- November 6, 2017:
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 … Continue reading
- October 10, 2017:
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 … Continue reading
- September 8, 2017:
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 … Continue reading
- September 1, 2017:
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 … Continue reading
- April 1, 2017:
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 … Continue reading
- January 13, 2017:
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 … Continue reading
- January 10, 2017:
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 … Continue reading
- October 24, 2016:
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 … Continue reading
- October 20, 2016:
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, … Continue reading
- September 26, 2016:
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 … Continue reading
- September 16, 2016:
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 … Continue reading
- September 14, 2016:
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 $\sum_n a_n$ … Continue reading
- September 2, 2016:
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 … Continue reading
- July 17, 2016:
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 … Continue reading
- March 28, 2016:
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 … Continue reading
- March 3, 2016:
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 … Continue reading
- January 7, 2016:
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 … Continue reading
- November 10, 2015:
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 … Continue reading
- October 2, 2015:
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 … Continue reading
- September 16, 2015:
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 … Continue reading
- September 7, 2015:
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 … Continue reading
- July 7, 2015:
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 … Continue reading
- May 30, 2015:
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 … Continue reading
- April 30, 2015:
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 … Continue reading
- April 27, 2015:
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 … Continue reading
- March 6, 2015:
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. … Continue reading
- January 5, 2015:
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.) … Continue reading
- December 5, 2014:
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 … Continue reading
- November 21, 2014:
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 … Continue reading
- November 10, 2014:
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 … Continue reading
- October 25, 2014:
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 … Continue reading
- October 18, 2014:
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 … Continue reading
- October 10, 2014:
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 … Continue reading
- October 3, 2014:
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 … Continue reading
- July 9, 2014:
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 … Continue reading
- June 20, 2014:
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 … Continue reading
- June 18, 2014:
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 … Continue reading
- May 23, 2014:
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 … Continue reading
- May 19, 2014:
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 … Continue reading
- April 21, 2014:
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 … Continue reading
- February 4, 2014:
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 … Continue reading
- January 31, 2014:
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 … Continue reading
- January 23, 2014:
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 … Continue reading
- January 23, 2014:
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 … Continue reading
- January 18, 2014:
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 … Continue reading
- November 14, 2013:
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 … Continue reading
- October 31, 2013:
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 … Continue reading
- October 26, 2013:
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 … Continue reading
- October 25, 2013:
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 … Continue reading
- October 15, 2013:
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 … Continue reading
- October 8, 2013:
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 … Continue reading
- September 27, 2013:
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 … Continue reading
- September 20, 2013:
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 … Continue reading
- August 30, 2013:
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 … Continue reading
- June 15, 2013:
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 … Continue reading
- June 13, 2013:
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 … Continue reading
- June 11, 2013:
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 … Continue reading
- June 1, 2013:
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 … Continue reading
- May 10, 2013:
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, … Continue reading
- April 30, 2013:
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 … Continue reading
- March 25, 2013:
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 … Continue reading
- March 1, 2013:
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 … Continue reading
- February 15, 2013:
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 … Continue reading
- February 1, 2013:
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 … Continue reading
- December 15, 2012:
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 … Continue reading
- November 28, 2012:
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 … Continue reading
- November 19, 2012:
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 … Continue reading
- September 14, 2012:
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, … Continue reading
- September 7, 2012:
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 … Continue reading
- August 24, 2012:
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. … Continue reading
- June 23, 2012:
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 … Continue reading
- June 15, 2012:
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 … Continue reading
- May 18, 2012:
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 … Continue reading
- May 18, 2012:
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 … Continue reading
- April 24, 2012:
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 … Continue reading
- April 23, 2012:
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, … Continue reading
- April 18, 2012:
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 … Continue reading
- April 17, 2012:
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 … Continue reading
- November 4, 2011:
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 … Continue reading
- November 3, 2011:
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, … Continue reading
- August 1, 2011:
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 … Continue reading
- April 22, 2011:
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, … Continue reading