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Martin's Axiom Luzin set Hereditarily Lindelöf space Almost countably chromatic very good scale Generalized descriptive set theory Cohen real Axiom R strongly bounded groups Forcing Coherent tree Fast club Iterated forcing free Boolean algebra Souslin Tree Diamond-sharp Large Cardinals C-sequence Selective Ultrafilter Forcing Axioms Greatly Mahlo Intersection model Uniformization Open Access coloring number Constructible Universe Commutative projection system Whitehead Problem Subadditive PFA Almost-disjoint family Analytic sets Microscopic Approach 54G20 Local Club Condensation. Small forcing Filter reflection Minimal Walks Commutative cancellative semigroups Lipschitz reduction Respecting tree Subtle tree property ccc Absoluteness Successor of Regular Cardinal Erdos Cardinal square principles projective Boolean algebra OCA Hedetniemi's conjecture Chromatic number Nonspecial tree Sakurai's Bell inequality Subtle cardinal reflection principles Chang's conjecture Amenable C-sequence ZFC construction stationary hitting Generalized Clubs Rock n' Roll SNR Square-Brackets Partition Relations higher Baire space Countryman line nonmeager set full tree Singular cardinals combinatorics Sierpinski's onto mapping principle Closed coloring Parameterized proxy principle Successor of Singular Cardinal O-space specializable Souslin tree diamond star Jonsson cardinal Dowker space Reflecting stationary set Dushnik-Miller Precaliber Knaster Rado's conjecture GMA Ramsey theory over partitions Erdos-Hajnal graphs Postprocessing function Knaster and friends Strongly Luzin set Poset L-space Cardinal Invariants free Souslin tree Was Ulam right? Cardinal function Slim tree super-Souslin tree Ascent Path Fodor-type reflection unbounded function Universal Sequences AIM forcing tensor product graph weak Kurepa tree positive partition relation HOD Strong coloring Aronszajn tree S-Space Vanishing levels Hindman's Theorem Ulam matrix Diamond for trees Uniformly coherent square Almost Souslin PFA(S)[S] countably metacompact indecomposable ultrafilter Diamond middle diamond Foundations Partition Relations Singular cofinality sap Fat stationary set Non-saturation stationary reflection Mandelbrot set weak diamond regressive Souslin tree Reduced Power Uniformly homogeneous Ineffable cardinal incompactness stick Antichain xbox Weakly compact cardinal b-scale Ostaszewski square weak square Club Guessing transformations Prevalent singular cardinals approachability ideal P-Ideal Dichotomy club_AD Kurepa Hypothesis Prikry-type forcing Strongly compact cardinal Sigma-Prikry Shelah's Strong Hypothesis Singular Density Distributive tree polarized partition relation Rainbow sets Well-behaved magma Subnormal ideal
Category Archives: Invited Talks
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
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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
Posted in Invited Talks
Tagged Ulam matrix, Was Ulam right?
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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
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MFO workshop in Set Theory, April 2020
The Set Theory workshop in Obwerwolfach was supposed to take place April 2020, but was transformed into a webinar, due to COVID-19. Here you will find the title, abstract, slides and video of my webinar talk. Talk Title: Transformations of … Continue reading
Posted in Invited Talks
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The 15th International Workshop on Set Theory in Luminy, September 2019
I gave an invited talk at the 15th International Workshop on Set Theory in Luminy in Marseille, September 2019. Talk Title: Chain conditions, unbounded colorings and the C-sequence spectrum. Abstract: The productivity of the $\kappa$-chain condition, where $\kappa$ is a regular, … Continue reading
Posted in Invited Talks
Tagged Closed coloring, Knaster, Precaliber, stationary reflection, unbounded function
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50 Years of Set Theory in Toronto, May 2019
I gave an invited talk at the 50 Years of Set Theory in Toronto meeting, Fields Institute for Research in Mathematical Sciences, May 2019. Talk Title: Analytic quasi-orders and two forms of diamond Abstract: We study Borel reduction of equivalence relations … Continue reading
Posted in Invited Talks
Tagged Analytic sets, Diamond-sharp, Generalized descriptive set theory
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