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