nylogic profile | set theory talks profile

- 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 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
- 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