Archives
Keywords
Small forcing Foundations Dushnik-Miller Cardinal Invariants Lipschitz reduction Souslin Tree P-Ideal Dichotomy PFA(S)[S] Prikry-type forcing Constructible Universe Generalized descriptive set theory Uniformly coherent Knaster and friends ccc Diamond Intersection model diamond star stationary hitting Strongly compact cardinal very good scale Countryman line Ascending path Selective Ultrafilter Forcing Axioms Kurepa Hypothesis Singular Density full tree Microscopic Approach Strong coloring Respecting tree Uniformization approachability ideal Entangled linear order tensor product graph PFA Forcing with side conditions Successor of Regular Cardinal club_AD square Poset Luzin set Rock n' Roll weak square Cohen real Ineffable cardinal Universal Sequences Vanishing levels Jonsson cardinal Partition Relations free Boolean algebra Open Access Ascent Path Singular cardinals combinatorics Rado's conjecture b-scale Hereditarily Lindelöf space SNR Non-saturation Sierpinski's onto mapping principle Club Guessing Hedetniemi's conjecture Absoluteness Nonspecial tree Almost-disjoint family Chang's conjecture Commutative projection system Closed coloring Subnormal ideal Knaster Analytic sets Commutative cancellative semigroups reflection principles Ulam matrix Ramsey theory over partitions xbox Martin's Axiom Slim tree Distributive tree Shelah's Strong Hypothesis O-space Subtle cardinal Almost countably chromatic square principles Interval topology on trees Fodor-type reflection Diamond-sharp weak Kurepa tree Diamond for trees Monotonically far indecomposable filter Well-behaved magma Local Club Condensation. Erdos-Hajnal graphs Greatly Mahlo strongly bounded groups unbounded function Rainbow sets Parameterized proxy principle stationary reflection Strongly Luzin set Mandelbrot set Subtle tree property Antichain AIM forcing Singular cofinality countably metacompact Amenable C-sequence Cardinal function Prevalent singular cardinals L-space Coherent tree Reduced Power Large Cardinals Ostaszewski square Forcing Whitehead Problem specializable Souslin tree Axiom R Precaliber Almost Souslin Dowker space Minimal Walks Sakurai's Bell inequality middle diamond Was Ulam right? projective Boolean algebra regressive Souslin tree Erdos Cardinal Iterated forcing ZFC construction C-sequence Hindman's Theorem free Souslin tree Filter reflection perfectly normal higher Baire space coloring number Aronszajn tree nonmeager set polarized partition relation Square-Brackets Partition Relations Chromatic number Successor of Singular Cardinal Subadditive weak diamond Postprocessing function Fat stationary set S-Space Fast club HOD OCA GMA super-Souslin tree Reflecting stationary set incompactness sap stick Generalized Clubs positive partition relation transformations Weakly compact cardinal Uniformly homogeneous Sigma-Prikry 54G20 Partition relations for trees
Category Archives: Invited Talks
40th summer conference on topology and its applications
I gave an invited talk at the General and Set-Theoretic Topology session of the 40th summer conference on topology and its applications, July 2026. Talk title: A tree-based perfectly normal space whose square is not countably metacompact. Abstract. The study … Continue reading
Posted in Invited Talks, Topology
Tagged Interval topology on trees
Comments Off on 40th summer conference on topology and its applications
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
