Archives
Keywords
sap stationary reflection weak Kurepa tree Antichain Rado's conjecture Poset Generalized descriptive set theory Diamond square principles countably metacompact Almost-disjoint family transformations weak square Vanishing levels Precaliber Uniformly homogeneous super-Souslin tree Fodor-type reflection higher Baire space full tree Partition Relations Microscopic Approach Subadditive Sierpinski's onto mapping principle stick Ascending path Chromatic number Commutative cancellative semigroups Strongly Luzin set Uniformly coherent L-space Fast club club_AD Reduced Power Closed coloring regressive Souslin tree Ostaszewski square Prevalent singular cardinals polarized partition relation coloring number Constructible Universe Forcing with side conditions Was Ulam right? Almost Souslin Intersection model Fat stationary set Ramsey theory over partitions Whitehead Problem Successor of Regular Cardinal diamond star Sigma-Prikry Non-saturation Singular Density ZFC construction Subtle tree property perfectly normal indecomposable filter free Boolean algebra PFA(S)[S] Interval topology on trees Minimal Walks Cardinal Invariants Shelah's Strong Hypothesis Nonspecial tree Cardinal function Monotonically far reflection principles PFA Selective Ultrafilter xbox free Souslin tree specializable Souslin tree Ascent Path Commutative projection system very good scale Knaster and friends Absoluteness Martin's Axiom OCA strongly bounded groups AIM forcing Subtle cardinal Coherent tree Hindman's Theorem Square-Brackets Partition Relations Local Club Condensation. Amenable C-sequence Knaster HOD Dowker space Diamond for trees Lipschitz reduction Large Cardinals Successor of Singular Cardinal square Cohen real Sakurai's Bell inequality Greatly Mahlo Strong coloring Dushnik-Miller Open Access Generalized Clubs projective Boolean algebra Singular cardinals combinatorics unbounded function Respecting tree Weakly compact cardinal Rock n' Roll Reflecting stationary set b-scale Ineffable cardinal Almost countably chromatic Uniformization Hedetniemi's conjecture Prikry-type forcing Souslin Tree Luzin set O-space 54G20 C-sequence Filter reflection Analytic sets Diamond-sharp approachability ideal Subnormal ideal tensor product graph S-Space Countryman line SNR Universal Sequences weak diamond Slim tree Kurepa Hypothesis positive partition relation Foundations Rainbow sets middle diamond Forcing Axioms Postprocessing function Erdos-Hajnal graphs Forcing Club Guessing Small forcing Iterated forcing Axiom R Aronszajn tree Hereditarily Lindelöf space Parameterized proxy principle Mandelbrot set GMA Entangled linear order Ulam matrix Erdos Cardinal incompactness ccc Chang's conjecture Well-behaved magma Partition relations for trees stationary hitting Singular cofinality P-Ideal Dichotomy Strongly compact cardinal nonmeager set Distributive tree Jonsson cardinal
Category Archives: Invited Talks
The 18th International Workshop on Set Theory in Luminy, November 2015
I gave an invited talk at the 18th International Workshop on Set Theory in Luminy in Marseille, November 2025. Talk Title: What is a higher forcing axiom? Abstract: There are multiple interpretations of what is a forcing axiom. We shall … Continue reading
Posted in Invited Talks
Tagged Forcing Axioms
Comments Off on The 18th International Workshop on Set Theory in Luminy, November 2015
Conference in honor of Saharon Shelah’s 80th birthday
I gave an invited talk at the conference in honor of Shelah’s 80th birthday, July 2025. Talk Title: Marginalia to [Sh:365] Abstract: Solovay famously proved that every stationary subset of a regular uncountable cardinal kappa may be decomposed into kappa … Continue reading
Posted in Invited Talks
Tagged Greatly Mahlo, Strong coloring, Was Ulam right?
Comments Off on Conference in honor of Saharon Shelah’s 80th birthday
2025 Annual conference of the IMU
I gave an invited talk at the Set Theory session of the annual meeting of the IMU, July 2025. Talk Title: What my co-authors taught me about indecomposability Abstract: Ulam’s measure problem studies when there is a countably-additive two-valued measure … Continue reading
Posted in Invited Talks
Tagged indecomposable filter
Comments Off on 2025 Annual conference of the IMU
MFO workshop in Set Theory, January 2025
I gave an invited talk at the Set Theory meeting in Obwerwolfach, January 2025. Talk Title: Non-structure theorems for higher Aronszajn lines. Abstract: An $\omega_1$-Countryman line is an uncountable linear order $L$ such that $L^2$ (with the pointwise ordering) is … Continue reading
Posted in Invited Talks
Tagged Countryman line, Monotonically far
Comments Off on MFO workshop in Set Theory, January 2025
120 Years of Choice, July 2024
I gave an invited talk at the 120 Years of Choice conference, July 2024. Talk Title: Mathematician’s best friend Abstract: Jensen’s diamond is a very useful postulate. It is well-known that it implies the continuum hypothesis, that it is equivalent … Continue reading
Perspectives on Set Theory, November 2023
I gave an invited talk at the Perspectives on Set Theory conference, November 2023. Talk Title: May the successor of a singular cardinal be Jónsson? Abstract: We’ll survey what’s known about the question in the title and collect ten open … Continue reading
Posted in Invited Talks, Open Problems
Tagged Jonsson cardinal, Successor of Singular Cardinal
Comments Off on Perspectives on Set Theory, November 2023
Gdańsk Logic Conference, May 2023
I gave an invited talk at the first Gdańsk Logic Conference, May 2023. Talk Title: Was Ulam right? Abstract: An Ulam matrix is one of the earliest gems of infinite combinatorics. Around the same time of its discovery, another Polish … Continue reading
A series of lectures on Club_AD, February–March 2023
As part of the Thematic Program on Set Theoretic Methods in Algebra, Dynamics and Geometry (Fields Institute, January–June, 2023), Spencer Unger and I delivered a Graduate Course on Set Theory, Algebra and Analysis. My part of the course was a … Continue reading
Winter School in Abstract Analysis, January 2023
I gave a 3-lecture tutorial at the Winter School in Abstract Analysis in Steken, January 2023. Title: Club guessing Abstract. Club guessing principles were introduced by Shelah as a weakening of Jensen’s diamond. Most spectacularly, they were used to prove … Continue reading
MFO workshop in Set Theory, January 2022
I gave an invited talk at the Set Theory meeting in Obwerwolfach, January 2022. Talk Title: A dual of Juhasz’ question Abstract: Juhasz asked whether $\clubsuit$ implies the existence of a Souslin tree. Here we settle the dual problem of … Continue reading
Posted in Invited Talks
Tagged club_AD, Dowker space
Comments Off on MFO workshop in Set Theory, January 2022
