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