_{January 18, 2024}

Parameter-free schemes in second-order arithmetic

_{December 19, 2023}

Cardinal correct extendible cardinals

_{December 18, 2023}

New large cardinal chart of Ramsey-like cardinals

_{December 14, 2023}

Upward Löwenheim-Skolem numbers for abstract logics

_{November 20, 2023}

Between Ramsey and measurable cardinals

_{November 10, 2023}

Upward Löwenheim-Skolem numbers for abstract logics

_{July 21, 2023}

An overview of virtual large cardinals

_{July 21, 2023}

A gentle introduction to class forcing

_{May 01, 2023}

Jensen forcing at an inaccessible and a model of Kelley-Morse satisfying ${\rm CC}$ but not ${\rm DC}_\omega$

_{April 10, 2023}

Jensen’s forcing at an inaccessible

_{March 24, 2023}

Parameter-free comprehension in second-order arithmetic

_{February 22, 2023}

Working in set theory without powerset

_{August 21, 2022}

A version of Jensen's forcing for an inaccessible cardinal

_{August 15, 2022}

Can a Cohen extension have an $\omega_1$-sequence of successively more generic Cohen reals?

_{August 03, 2022}

ZFC without Power Set II: Reflection Strikes Back

_{November 10, 2021}

Set theory without powerset

_{September 28, 2021}

Indestructibility for Ramsey cardinals

_{September 14, 2021}

Jensen's forcing at an inaccessible

_{September 01, 2021}

Indestructibility for Ramsey and Ramsey-like cardinals

_{July 14, 2021}

Characterizing large cardinals via abstract logics

_{June 25, 2021}

The many universes of modern set theory

_{June 17, 2021}

Characterizing large cardinals via abstract logics

_{June 11, 2021}

The old and the new of virtual large cardinals

_{December 16, 2020}

Characterizing large cardinals via abstract logics

_{October 28, 2020}

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

_{October 09, 2020}

Model theoretic characterizations of large cardinals revisited

_{September 08, 2020}

The virtual large cardinal hierarchy

_{August 10, 2020}

Abstract Logics

_{June 25, 2020}

Class forcing in its rightful setting

_{May 06, 2020}

Elementary embeddings and smaller large cardinals

_{January 10, 2020}

Toy multiverses of set theory

_{January 10, 2020}

Ramsey-like cardinals

_{November 13, 2019}

Modern class forcing

_{October 10, 2019}

Structural properties of the stable core

_{October 10, 2019}

Ground model definability in ${\rm ZF}$

_{July 17, 2019}

Toy multiverses of set theory

_{July 16, 2019}

Computably saturated models of ZFC

_{June 04, 2019}

Some cute observations about computably saturated models

_{April 26, 2019}

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

_{April 19, 2019}

Set theory in second-order

_{April 11, 2019}

Set theories with classes

_{April 11, 2019}

Kelley-Morse set theory does not prove the class Fodor principle

_{April 11, 2019}

A primer on the set-theoretic multiverse

_{February 19, 2019}

Forcing a $\square(\kappa)$-like principle to hold at a weakly compact cardinal

_{October 15, 2018}

The Stable Core

_{September 11, 2018}

The Stable Core

_{July 15, 2018}

Virtual Vopěnka's Principle

_{May 20, 2018}

Boolean-valued class forcing

_{May 01, 2018}

Boolean-valued class forcing

_{March 21, 2018}

Virtual large cardinal principles at KGRC

_{March 21, 2018}

A model of second-order arithmetic satisfying AC but not DC

_{January 03, 2018}

The emerging zoo of second-order set theories

_{October 12, 2017}

Virtual large cardinal principles

_{September 27, 2017}

Filter games and Ramsey-like cardinals

_{July 13, 2017}

The exact strength of the class forcing theorem

_{July 13, 2017}

A model of the generic Vopěnka principle in which the ordinals are not Mahlo

_{May 09, 2017}

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

_{March 15, 2017}

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

_{March 14, 2017}

Virtual large cardinals

_{March 06, 2017}

Virtual Set Theory and Generic Vopěnka's Principle

_{January 20, 2017}

A countable ordinal definable set of reals without ordinal definable elements

_{December 06, 2016}

The oddities of class forcing

_{September 10, 2016}

A set-theoretic approach to Scott's Problem

_{May 17, 2016}

Generic Vopěnka's Principle at YST2016

_{April 19, 2016}

Generic Vopěnka's Principle

_{March 29, 2016}

Computable processes can produce arbitrary outputs in nonstandard models

_{March 29, 2016}

Computable processes can produce arbitrary outputs in nonstandard models (continued)

_{February 25, 2016}

Virtual large cardinals

_{February 10, 2016}

Generic Vopěnka's Principle, remarkable cardinals, and the weak Proper Forcing Axiom

_{January 05, 2016}

Set Theory Day to celebrate Joel David Hamkins' 50th birthday

_{October 23, 2015}

Mitchell order for Ramsey and Ramsey-like cardinals

_{September 10, 2015}

Open determinacy for class games

_{July 31, 2015}

Ehrenfeucht principles in set theory

_{July 20, 2015}

Indestructible remarkable cardinals

_{May 07, 2015}

My first Black Board Day

_{April 22, 2015}

An introduction to nonstandard models of arithmetic

_{February 19, 2015}

Remarkable Laver functions

_{January 09, 2015}

Ehrenfeucht's lemma in set theory

_{December 31, 2014}

Kelley-Morse set theory and choice principles for classes

_{October 23, 2014}

Separating the choice scheme from the parameter-free choice scheme in second-order arithmetic

_{September 17, 2014}

Indestructibility properties of remarkable cardinals

_{September 17, 2014}

Incomparable $\omega_1$-like models of set theory

_{August 07, 2014}

Co-organizing the CUNY Set Theory Seminar

_{July 30, 2014}

Choice schemes for Kelley-Morse set theory

_{May 07, 2014}

An absoluteness lemma for countable embeddings

_{March 17, 2014}

Incomparable $\omega_1$-like models of set theory

_{March 01, 2014}

Introduction to remarkable cardinals

_{February 24, 2014}

Variants of Kelley-Morse set theory

_{January 29, 2014}

Ramsey cardinals and the continuum function

_{November 13, 2013}

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

_{October 12, 2013}

Forcing to add proper classes to a model of ${\rm GBC}$: The technicalities

_{October 09, 2013}

Forcing to add proper classes to a model of ${\rm GBC}$: An introduction

_{October 01, 2013}

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

_{June 28, 2013}

Large cardinal chart of Ramsey-like cardinals

_{June 25, 2013}

On ground model definability

_{February 01, 2013}

Mathematical Logic Course

_{September 03, 2012}

Easton's theorem for Ramsey and strongly Ramsey cardinals

_{July 31, 2012}

Who let the zombies out?

_{April 18, 2012}

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

_{March 01, 2012}

Indestructibility for Ramsey cardinals

_{January 18, 2012}

An iPhone app for a nonstandard model of number theory?

_{December 09, 2011}

What is the theory ZFC without power set?

_{November 10, 2011}

Inner models with large cardinal features usually obtained by forcing

_{November 03, 2011}

Forcing and gaps in $2^\omega$

_{March 31, 2010}

A natural model of the multiverse axioms

_{March 26, 2010}

A natural model of the multiverse axioms

_{January 01, 2010}

Gödel's Proof

_{October 28, 2009}

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

_{July 31, 2009}

Ramsey-like cardinals II

_{July 31, 2009}

Ramsey-like cardinals

_{July 31, 2008}

Proper and piecewise proper families of reals

_{June 01, 2008}

Scott’s problem for proper Scott sets

_{June 01, 2008}

Applications of the proper forcing axiom to models of Peano Arithmetic