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