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