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Antichain Singular cofinality weak square Intersection model Hereditarily Lindelöf space Was Ulam right SNR countably metacompact diamond star Foundations ccc Ascent Path Sierpinski's onto mapping principle higher Baire space positive partition relation Sigma-Prikry Poset Dowker space Commutative projection system Subnormal ideal Absoluteness Fodor-type reflection Closed coloring full tree Parameterized proxy principle Distributive tree Jonsson cardinal Slim tree club_AD C-sequence stationary reflection projective Boolean algebra PFA Lipschitz reduction free Boolean algebra indecomposable ultrafilter Martin's Axiom Uniformly coherent Commutative cancellative semigroups polarized partition relation Souslin Tree Kurepa Hypothesis Singular Density Cohen real Generalized Clubs square principles Postprocessing function Erdos Cardinal 54G20 Iterated forcing Uniformization Rado's conjecture Whitehead Problem regressive Souslin tree Almost Souslin reflection principles stick Greatly Mahlo Small forcing Minimal Walks Strongly Luzin set tensor product graph Constructible Universe Axiom R Partition Relations Reduced Power Ulam matrix free Souslin tree b-scale Diamond for trees Fast club Countryman line Open Access Knaster and friends HOD coloring number transformations weak diamond Forcing Axioms Local Club Condensation. Successor of Singular Cardinal Knaster Fat stationary set GMA Amenable C-sequence Chang's conjecture super-Souslin tree Reflecting stationary set specializable Souslin tree OCA Erdos-Hajnal graphs unbounded function Almost countably chromatic approachability ideal sap incompactness nonmeager set Large Cardinals Nonspecial tree Subadditive P-Ideal Dichotomy Cardinal Invariants Mandelbrot set Forcing PFA(S)[S] Vanishing levels Luzin set Hedetniemi's conjecture Club Guessing Selective Ultrafilter Universal Sequences Prevalent singular cardinals Diamond-sharp Shelah's Strong Hypothesis Analytic sets Ramsey theory over partitions Rainbow sets Microscopic Approach Diamond AIM forcing weak Kurepa tree Precaliber S-Space Hindman's Theorem Non-saturation square Generalized descriptive set theory ZFC construction xbox Successor of Regular Cardinal Respecting tree very good scale Almost-disjoint family Sakurai's Bell inequality Prikry-type forcing middle diamond Weakly compact cardinal Subtle cardinal Well-behaved magma Square-Brackets Partition Relations Strongly compact cardinal strongly bounded groups Coherent tree O-space Strong coloring Dushnik-Miller Aronszajn tree Filter reflection Chromatic number Subtle tree property Uniformly homogeneous Rock n' Roll Ineffable cardinal Singular cardinals combinatorics stationary hitting L-space Ostaszewski square Cardinal function
Tag Archives: Sierpinski’s onto mapping principle
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
Ramsey theory over partitions III: Strongly Luzin sets and partition relations
Joint work with Menachem Kojman and Juris Steprāns. Abstract. The strongest type of coloring of pairs of countable ordinals, gotten by Todorcevic from a strongly Luzin set, is shown to be equivalent to the existence of a nonmeager set of … Continue reading
Jones’ theorem on the cardinal invariant $\mathfrak p$
This post continues the study of the cardinal invariant $\mathfrak p$. We refer the reader to a previous post for all the needed background. For ordinals $\alpha,\alpha_0,\alpha_1,\beta,\beta_0,\beta_1$, the polarized partition relation $$\left(\begin{array}{c}\alpha\\\beta\end{array}\right)\rightarrow\left(\begin{array}{cc}\alpha_0&\alpha_1\\\beta_0&\beta_1\end{array}\right)$$ asserts that for every coloring $f:\alpha\times\beta\rightarrow 2$, (at least) … Continue reading
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Tagged polarized partition relation, Sierpinski's onto mapping principle
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