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reflection principles Filter reflection Whitehead Problem Local Club Condensation. projective Boolean algebra Commutative cancellative semigroups approachability ideal Almost Souslin Rainbow sets Fat stationary set Hindman's Theorem regressive Souslin tree square principles Singular cofinality Weakly compact cardinal Precaliber Sakurai's Bell inequality square Parameterized proxy principle Postprocessing function AIM forcing full tree Chromatic number S-Space Analytic sets strongly bounded groups Reflecting stationary set Poset OCA Square-Brackets Partition Relations Diamond-sharp Axiom R Cardinal function countably metacompact Cardinal Invariants diamond star Large Cardinals Club Guessing PFA(S)[S] Coherent tree club_AD free Souslin tree Fodor-type reflection Open Access very good scale Iterated forcing Successor of Singular Cardinal Knaster and friends Subtle cardinal Diamond C-sequence Distributive tree Erdos-Hajnal graphs L-space Cohen real stick Hedetniemi's conjecture Ulam matrix Diamond for trees Strongly Luzin set indecomposable ultrafilter Jonsson cardinal P-Ideal Dichotomy Subadditive Antichain Dushnik-Miller ZFC construction Was Ulam right Aronszajn tree Selective Ultrafilter GMA Sierpinski's onto mapping principle HOD sap Small forcing Ostaszewski square Uniformization Dowker space Luzin set Universal Sequences Generalized descriptive set theory Lipschitz reduction polarized partition relation O-space Microscopic Approach Absoluteness Foundations Ascent Path Partition Relations Prikry-type forcing Reduced Power Shelah's Strong Hypothesis Vanishing levels 54G20 Almost countably chromatic Almost-disjoint family Successor of Regular Cardinal Closed coloring weak diamond Subtle tree property Uniformly homogeneous Prevalent singular cardinals Martin's Axiom Forcing ccc Greatly Mahlo Well-behaved magma Singular cardinals combinatorics free Boolean algebra Souslin Tree Erdos Cardinal weak Kurepa tree Mandelbrot set Singular Density Slim tree PFA Amenable C-sequence Nonspecial tree coloring number SNR stationary reflection super-Souslin tree Kurepa Hypothesis Chang's conjecture Generalized Clubs Non-saturation middle diamond tensor product graph higher Baire space xbox Fast club Constructible Universe Rock n' Roll Minimal Walks Ineffable cardinal Ramsey theory over partitions Knaster specializable Souslin tree Uniformly coherent unbounded function positive partition relation Hereditarily Lindelöf space stationary hitting Forcing Axioms Sigma-Prikry Subnormal ideal nonmeager set weak square Strong coloring transformations Rado's conjecture incompactness b-scale
Tag Archives: Ulam matrix
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
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
Was Ulam right? II: Small width and general ideals
Joint work with Tanmay Inamdar. Abstract. We continue our study of Sierpinski-type colourings. In contrast to the prequel paper, we focus here on colourings for ideals stratified by their completeness degree. In particular, improving upon Ulam’s theorem and its extension … Continue reading
Posted in Partition Relations, Publications
Tagged 03E02, 03E35, 03E55, C-sequence, Open Access, Subnormal ideal, Ulam matrix, Was Ulam right
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Was Ulam right? I: Basic theory and subnormal ideals
Joint work with Tanmay Inamdar. Abstract. We introduce various coloring principles which generalize the so-called onto mapping principle of Sierpinski to larger cardinals and general ideals. We prove that these principles capture the notion of an Ulam matrix and allow … Continue reading
Partitioning a reflecting stationary set
Joint work with Maxwell Levine. Abstract. We address the question of whether a reflecting stationary set may be partitioned into two or more reflecting stationary subsets, providing various affirmative answers in ZFC. As an application to singular cardinals combinatorics, we infer … Continue reading
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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