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Prevalent singular cardinals Forcing Axioms Diamond for trees 54G20 Singular cardinals combinatorics weak diamond L-space Sierpinski's onto mapping principle free Boolean algebra Ineffable cardinal Whitehead Problem Diamond Microscopic Approach Kurepa Hypothesis Filter reflection Amenable C-sequence club_AD very good scale Vanishing levels PFA stationary reflection Closed coloring Dushnik-Miller Large Cardinals Subnormal ideal Antichain S-Space regressive Souslin tree nonmeager set AIM forcing Sakurai's Bell inequality Diamond-sharp Was Ulam right incompactness diamond star Minimal Walks Forcing Ulam matrix stationary hitting Precaliber countably metacompact higher Baire space Foundations Subtle tree property Dowker space GMA Fat stationary set square Rado's conjecture Square-Brackets Partition Relations Cardinal Invariants b-scale Local Club Condensation. Generalized Clubs Iterated forcing Lipschitz reduction Strongly Luzin set Axiom R Fast club Rock n' Roll projective Boolean algebra Subtle cardinal square principles Sigma-Prikry Ascent Path Parameterized proxy principle Open Access indecomposable ultrafilter Strong coloring SNR Cohen real C-sequence OCA Hereditarily Lindelöf space Hedetniemi's conjecture Constructible Universe Selective Ultrafilter ZFC construction sap Rainbow sets Singular Density PFA(S)[S] Ramsey theory over partitions Uniformly homogeneous positive partition relation Well-behaved magma strongly bounded groups Universal Sequences Nonspecial tree coloring number polarized partition relation Non-saturation Poset Luzin set xbox Singular cofinality Erdos-Hajnal graphs Jonsson cardinal Aronszajn tree Martin's Axiom ccc Successor of Singular Cardinal Distributive tree reflection principles Partition Relations Cardinal function Chromatic number Hindman's Theorem Commutative cancellative semigroups stick Club Guessing Greatly Mahlo Absoluteness Knaster Erdos Cardinal Weakly compact cardinal Analytic sets tensor product graph Slim tree middle diamond full tree Small forcing Uniformly coherent Almost Souslin weak Kurepa tree Fodor-type reflection Generalized descriptive set theory Knaster and friends Prikry-type forcing Reflecting stationary set unbounded function specializable Souslin tree super-Souslin tree P-Ideal Dichotomy Ostaszewski square Almost-disjoint family HOD Uniformization Postprocessing function free Souslin tree Mandelbrot set Almost countably chromatic weak square Coherent tree Souslin Tree transformations O-space Subadditive Reduced Power Chang's conjecture Shelah's Strong Hypothesis Successor of Regular Cardinal approachability ideal
Blog Archives
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
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Infinite Combinatorics Seminar, Haifa University, June, 2012
I gave a talk at the University of Haifa on June 07, 2012, intended for general audience. Title: Strong Colorings: the study of the failure of generalized Ramsey statements Abstract: A strong coloring from $X$ to $Y$ is a function … Continue reading
Posted in Contributed Talks
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