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square Was Ulam right Greatly Mahlo Square-Brackets Partition Relations strongly bounded groups PFA(S)[S] Generalized Clubs Strongly Luzin set Ostaszewski square Cardinal Invariants Constructible Universe Prikry-type forcing Parameterized proxy principle sap Iterated forcing Countryman line Martin's Axiom Souslin Tree Analytic sets PFA Minimal Walks Amenable C-sequence Diamond-sharp Hedetniemi's conjecture ZFC construction Rado's conjecture square principles unbounded function polarized partition relation Jonsson cardinal Commutative cancellative semigroups full tree Strongly compact cardinal Hereditarily Lindelöf space Subadditive Sigma-Prikry Local Club Condensation. specializable Souslin tree Foundations nonmeager set Coherent tree Reflecting stationary set O-space Large Cardinals Luzin set Kurepa Hypothesis Fat stationary set Slim tree weak diamond weak square Universal Sequences xbox Chang's conjecture Microscopic Approach Partition Relations transformations Cardinal function Poset Strong coloring Selective Ultrafilter Rock n' Roll Vanishing levels Precaliber Erdos-Hajnal graphs Ramsey theory over partitions Singular cardinals combinatorics Uniformization Forcing Axioms AIM forcing super-Souslin tree Fodor-type reflection Chromatic number Ineffable cardinal Rainbow sets Successor of Singular Cardinal Uniformly coherent Cohen real Ulam matrix Postprocessing function Sierpinski's onto mapping principle Distributive tree Whitehead Problem approachability ideal Mandelbrot set Singular Density Filter reflection stationary reflection SNR 54G20 Erdos Cardinal ccc Small forcing Club Guessing Subtle tree property Lipschitz reduction tensor product graph Reduced Power countably metacompact Knaster and friends free Boolean algebra positive partition relation Well-behaved magma Intersection model weak Kurepa tree Diamond Absoluteness P-Ideal Dichotomy stationary hitting Hindman's Theorem Sakurai's Bell inequality Aronszajn tree Almost countably chromatic higher Baire space Shelah's Strong Hypothesis HOD Closed coloring Antichain Forcing Respecting tree Open Access S-Space club_AD stick Weakly compact cardinal GMA Nonspecial tree indecomposable ultrafilter Subtle cardinal Almost Souslin regressive Souslin tree OCA L-space Commutative projection system Dushnik-Miller middle diamond Diamond for trees free Souslin tree diamond star Uniformly homogeneous b-scale C-sequence Singular cofinality Dowker space very good scale incompactness Prevalent singular cardinals Ascent Path Generalized descriptive set theory reflection principles Axiom R Almost-disjoint family coloring number Subnormal ideal Successor of Regular Cardinal Non-saturation projective Boolean algebra Fast club Knaster
Category Archives: Invited Talks
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
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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4th Arctic Set Theory Workshop, January 2019
I gave an invited talk at the Arctic Set Theory Workshop 4 in Kilpisjärvi, January 2019. Talk Title: Splitting a stationary set: Is there another way? Abstract: Motivated by a problem in pcf theory, we seek for a new way … Continue reading
Posted in Invited Talks
Tagged Club Guessing, Reflecting stationary set, Ulam matrix, very good scale
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