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