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- Prikry forcing may add a Souslin tree June 12, 2016
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Uniformization Forcing Rado's conjecture Minimal Walks incompactness b-scale Jonsson cardinal Microscopic Approach Large Cardinals Kurepa Hypothesis Uniformly coherent Ascent Path Non-saturation Prevalent singular cardinals polarized partition relation Cardinal Invariants weak diamond Prikry-type forcing Poset Hedetniemi's conjecture square principles Reduced Power super-Souslin tree 20M14 Dushnik-Miller Slim tree Almost Souslin Shelah's Strong Hypothesis Small forcing Weakly compact cardinal Selective Ultrafilter 05A17 xbox Chang's conjecture Cohen real Erdos Cardinal reflection principles Generalized Clubs Successor of Singular Cardinal Forcing Axioms Aronszajn tree Partition Relations Coherent tree Singular coﬁnality sap Rainbow sets stationary hitting HOD very good scale PFA(S)[S] Postprocessing function approachability ideal coloring number Almost countably chromatic stationary reflection Nonspecial tree square Singular Density Absoluteness diamond star Luzin set Parameterized proxy principle Commutative cancellative semigroups Almost-disjoint famiy Whitehead Problem projective Boolean algebra Chromatic number OCA Club Guessing Fast club S-Space middle diamond ccc Rock n' Roll Singular cardinals combinatorics Mandelbrot set Foundations Diamond Cardinal function Constructible Universe weak square Antichain Distributive tree Martin's Axiom PFA L-space Hereditarily Lindelöf space Knaster Sakurai's Bell inequality Hindman's Theorem Axiom R free Boolean algebra 11P99 Fat stationary set Universal Sequences P-Ideal Dichotomy Successor of Regular Cardinal Ostaszewski square Stevo Todorcevic Square-Brackets Partition Relations Fodor-type reflection Erdos-Hajnal graphs tensor product graph Souslin Tree

# 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