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