Talks

• Upward Löwenheim-Skolem numbers for abstract logics

  This is a talk at the CUNY Logic Workshop, CUNY Graduate Center, November 10, 2023.
  Slides

• An overview of virtual large cardinals

  This is a talk at the University of Konstanz, July 21, 2023.
  Slides

• A gentle introduction to class forcing

  This is a talk at the Konstanz Logik Kolloquium, University of Konstanz, July 21, 2023.
  Slides

• Jensen’s forcing at an inaccessible

  This is a talk at the Rutgers Logic Seminar, Rutgers University, April 10, 2023.
  Slides

• Parameter-free comprehension in second-order arithmetic

  This is a talk at the CUNY Logic Workshop, CUNY Graduate Center, March 24, 2023.
  Slides

• Working in set theory without powerset

  This is a talk at the Arctic Set Theory Workshop, University of Helsinki, February 22, 2023.
  Slides

• Set theory without powerset

  This is a talk at the Models and Sets Seminar, University of Leeds, November 10, 2021 (virtual).
  Slides

• Indestructibility for Ramsey cardinals

  This is a talk at the Minisymposium on ‘Large cardinals’, Joint Annual Conference of DMV and the ÖMG, University of Passau, September 28, 2021 (virtual).
  Slides

• Jensen's forcing at an inaccessible

  This is a talk at the 16th International Luminy Workshop in Set Theory, CIRM, September 14, 2021 (virtual).
  Slides

• Characterizing large cardinals via abstract logics

  This is a talk at the Münster Logic Seminar, University of Münster, July 14, 2021 (virtual).

• The many universes of modern set theory

  This is a talk at the Mathematics Colloquium, University of Warwick, June 25, 2021 (virtual).
  Slides

• Characterizing large cardinals via abstract logics

  This is a talk at the Boise extravaganza in set theory, University of Boise, June 17, 2021 (virtual).
  Slides

• The old and the new of virtual large cardinals

  This is a talk at the Turin-Udine Logic Seminar, University of Turin, June 11, 2021 (virtual).
  Slides Video

• Characterizing large cardinals via abstract logics

  This is a talk at the Barcelona Logic Seminar, University of Barcelona, December 16, 2020 (virtual).

• A model of second-order arithmetic satisfying ${\rm AC}$ but not ${\rm DC}$

  This is a talk at the MOPA Seminar, City University of New York, October 28 and November 4, 2020 (virtual).
  Slides Video 1 Video 2

• Class forcing in its rightful setting

  This is a talk at the Kurt Godel Research Seminar, University of Vienna, June 25, 2020 (virtual).
  Slides

• Elementary embeddings and smaller large cardinals

  This is a talk at the Oxford Logic Seminar, Oxford University, May 6, 2020 (virtual).
  Slides Video

• Toy multiverses of set theory

  This is a talk at the Winter ASL Meeting, Denver, January 17-18, 2020.

• Ramsey-like cardinals

  This is a talk at the Algebra and Logic Seminar, University of Denver, January 14, 2020.
  Slides

• Ground model definability in ${\rm ZF}$

  This is a talk at the Joint Mathematics Meeting, special session on 'Choiceless Set Theory and related areas', University of Denver, January 15-16, 2020.
  Slides

• Toy multiverses of set theory

  This is a talk at the Philosophy of Set Theory and Foundations workshop, University of Konstanz, August 1, 2019.
  Slides

• A model of second-order arithmetic satisfying ${\rm AC}$ but not ${\rm DC}$

  This is a talk at the Journées sur les Arithmétiques Faibles 2019 Conference, CUNY Graduate Center, May 28-30, 2019.
  Slides

• Set theory in second-order

  This is a talk at the Set Theory in UK 2 meeting, University of Bristol, May 8, 2019.

• Set theories with classes

  This is a talk at the special set theory session, Association for Symbolic Logic 2019 Annual North American Meeting, CUNY Graduate Center, May 20-23, 2019.
  Slides

• A primer on the set-theoretic multiverse

  This is a talk at the ALPS Seminar, Virginia Commonwealth University , April 12, 2019.
  Slides

• The Stable Core

  This is a talk at the Reflections on Set Theoretic Reflection Conference, University of Barcelona, November 16-19, 2018.

• The Stable Core

  This is a talk at the Mathematical Philosophy and Mathematical Practice Conference, University of Konstanz, September 20, 2018.
  Slides

• Virtual Vopěnka's Principle

  This is a talk at the Accessible categories and their connections Conference, University of Leeds, July 18, 2018.
  Slides

• Boolean-valued class forcing

  This is a talk at the CUNY Logic Workshop in New York, May 4, 2018.

• Virtual large cardinal principles at KGRC

  This is a talk at the Kurt Gödel Research Center Research Seminar in Vienna, Austria, April 14, 2018.
  Slides

• The emerging zoo of second-order set theories

  This is a talk at the Young Researchers' Workshop: Forcing and Philosophy, University of Konstanz, January 18, 2018.
  Slides

• Virtual large cardinal principles

  This is a talk at the Harvard Logic Colloquium, Cambridge, November 8, 2017.

• Filter games and Ramsey-like cardinals

  This is a talk at the CUNY Set Theory Seminar, October 20, 2017.

• A model of second-order arithmetic with the choice scheme in which $\Pi^1_2$-dependent choice fails

  This is a talk at the Kurt Gödel Research Center Research Seminar in Vienna, Austria, May 18, 2017.
  Slides

• Computable processes which produce any desired output in the right nonstandard model

  This is a talk at the special session "Computability Theory: Pushing the Boundaries" of 2​017 AMS Eastern Sectional Meeting in New York, May 6-7.

• Virtual Set Theory and Generic Vopěnka's Principle

  This is a talk at the VCU MAMLS Conference in Richmond, Virginia, April 1, 2017.

• A countable ordinal definable set of reals without ordinal definable elements

  This is a talk at the CUNY Set Theory Seminar, February 10, 2017.
  Notes

• A set-theoretic approach to Scott's Problem

  This is a talk at the National University of Singapore Logic Seminar, October 19, 2016.
  Slides

• Generic Vopěnka's Principle at YST2016

  This is a talk at the Young Set Theory 2016 Conference in Copenhagen, Denmark, June 13-17, 2016.

• Generic Vopěnka's Principle This is a talk at the Rutgers Logic Seminar in New Jersey, May 2, 2016.
• Computable processes can produce arbitrary outputs in nonstandard models

  This is a talk at the CUNY MOPA Seminar in New York, April 13, 2016.

• Virtual large cardinals

  This is a talk at Set Theory Day in New York, March 11, 2016.

• Ehrenfeucht principles in set theory

  This is a talk at the British Logic Colloquium in Cambridge, UK, September 2-4, 2015.
  Slides

• Indestructible remarkable cardinals

  This is a talk at the 5th European Set Theory Conference in Cambridge, UK, August 24-28, 2015.
  Slides

• An introduction to nonstandard models of arithmetic

  This is a talk at the Virginia Commonwealth University Analysis, Logic and Physics Seminar, April 24, 2015.
  Slides

• Remarkable Laver functions

  This is a talk at the CUNY Set Theory Seminar, February 27, 2015.

• Kelley-Morse set theory and choice principles for classes

  This is a talk at the SoTFoM II (Symposia on the Foundations of Mathematics) conference in London, UK, January 12-13, 2015.
  Slides

• Choice schemes for Kelley-Morse set theory

  This is a talk at the Colloquium Logicum Conference in Munich, Germany, September 4-6, 2014.
  Slides

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

  This is a talk at the Connecticut Logic Seminar, March 31, 2014.
  Slides

• Introduction to remarkable cardinals

  This is a talk at the CUNY Set Theory Seminar, March 14, 2014.

• Ramsey cardinals and the continuum function

  This is a talk at the CUNY Logic Workshop, February 14, 2014.
  Slides

• A Jonsson $\omega_1$-like model of set theory

  This is a talk at the CUNY Set Theory Seminar, November 15, 2013.

• Embeddings among $\omega_1$-like models of set theory

  This is a talk at the CUNY Set Theory Seminar, October 4, 2013.

• Models of $\rm{ZFC}^-$ that are not definable in their set forcing extensions

  This is a talk at the CUNY Set Theory Seminar, May 4, 2012.

• Indestructibility for Ramsey cardinals

  This is a talk at the Rutgers Logic Seminar, April 2, 2012.
  Slides

• An iPhone app for a nonstandard model of number theory?

  This is a talk at the City Tech C-LAC (Center for Logic, Algebra, and Computation) Seminar, February 14, 2012.
  Slides

• Forcing and gaps in $2^\omega$

  This is a talk at the CUNY Set Theory Seminar, December 2nd, 2011.
  Notes

• A natural model of the multiverse axioms

  This is a talk at the MIT Logic Seminar, April 8, 2010.
  Slides

• Gödel's Proof

  This is a talk at the United States Military Academy at West Point Mathematics Seminar, January 20, 2010.
  Slides

• Making strong cardinals indestructible by $\leq\kappa$-weakly closed Prikry forcing

  This was a talk at the CUNY Set Theory Seminar sometime in 2009.