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