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Coherent tree Singular Density Rado's conjecture Lipschitz reduction very good scale Generalized descriptive set theory incompactness Diamond for trees Prikry-type forcing Martin's Axiom Countryman line Weakly compact cardinal Rainbow sets Uniformly homogeneous Uniformization b-scale Uniformly coherent Erdos-Hajnal graphs Almost-disjoint family Small forcing coloring number Kurepa Hypothesis xbox Club Guessing Diamond-sharp PFA(S)[S] Successor of Singular Cardinal Strongly Luzin set Ramsey theory over partitions Chang's conjecture Iterated forcing Partition relations for trees P-Ideal Dichotomy Interval topology on trees Knaster and friends nonmeager set Precaliber Subtle tree property ZFC construction positive partition relation AIM forcing polarized partition relation tensor product graph SNR weak square stationary reflection Reduced Power Commutative projection system Distributive tree Well-behaved magma Hindman's Theorem regressive Souslin tree countably metacompact transformations Cardinal function Greatly Mahlo super-Souslin tree Reflecting stationary set Constructible Universe Universal Sequences Vanishing levels Nonspecial tree Subadditive Microscopic Approach Forcing Axioms Cardinal Invariants unbounded function Postprocessing function Forcing with side conditions Knaster indecomposable filter Fodor-type reflection Subnormal ideal free Boolean algebra Shelah's Strong Hypothesis middle diamond full tree Souslin Tree Parameterized proxy principle weak Kurepa tree Was Ulam right? Luzin set strongly bounded groups Minimal Walks Forcing Sigma-Prikry club_AD Rock n' Roll Ascending path OCA Dushnik-Miller reflection principles Hedetniemi's conjecture stationary hitting GMA PFA higher Baire space Whitehead Problem Absoluteness Almost Souslin Fast club Cohen real Monotonically far Fat stationary set L-space Respecting tree Partition Relations Entangled linear order Successor of Regular Cardinal free Souslin tree specializable Souslin tree Ineffable cardinal Large Cardinals Intersection model projective Boolean algebra square principles C-sequence Antichain HOD Foundations perfectly normal approachability ideal Poset Commutative cancellative semigroups Analytic sets 54G20 weak diamond S-Space Local Club Condensation. Non-saturation Ostaszewski square Diamond O-space Ulam matrix Axiom R ccc Singular cardinals combinatorics Open Access square Closed coloring stick Square-Brackets Partition Relations Strongly compact cardinal Jonsson cardinal Subtle cardinal Generalized Clubs Sakurai's Bell inequality Ascent Path Erdos Cardinal Amenable C-sequence Singular cofinality Almost countably chromatic Strong coloring sap diamond star Slim tree Chromatic number Mandelbrot set Dowker space Filter reflection Sierpinski's onto mapping principle Aronszajn tree Hereditarily Lindelöf space Selective Ultrafilter Prevalent singular cardinals
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
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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
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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?
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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
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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
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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
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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
