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- Prikry forcing may add a Souslin tree June 12, 2016
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stationary hitting Hereditarily Lindelöf space diamond star PFA Commutative cancellative semigroups sap Almost Souslin Coherent tree Fat stationary set Uniformization Singular Density free Boolean algebra Cardinal Invariants Ostaszewski square 20M14 05A17 Shelah's Strong Hypothesis Constructible Universe tensor product graph Partition Relations Fodor-type reflection Rainbow sets Whitehead Problem Ascent Path Small forcing S-Space Forcing Diamond Universal Sequences Jonsson cardinal Club Guessing Hedetniemi's conjecture Knaster ccc OCA Erdos Cardinal Axiom R square Martin's Axiom Slim tree Kurepa Hypothesis Cohen real xbox square principles HOD Parameterized proxy principle PFA(S)[S] polarized partition relation Chromatic number b-scale Selective Ultrafilter Poset Rado's conjecture weak diamond Prikry-type forcing Microscopic Approach Square-Brackets Partition Relations Singular coﬁnality Large Cardinals Souslin Tree stationary reflection approachability ideal P-Ideal Dichotomy middle diamond reflection principles Hindman's Theorem Almost-disjoint famiy Absoluteness 11P99 Postprocessing function Singular cardinals combinatorics Antichain weak square Cardinal function Uniformly coherent Distributive tree 05D10 coloring number Minimal Walks Chang's conjecture Aronszajn tree very good scale Reduced Power Sakurai's Bell inequality Successor of Regular Cardinal Nonspecial tree L-space Stevo Todorcevic Weakly compact cardinal incompactness Prevalent singular cardinals Almost countably chromatic Forcing Axioms Rock n' Roll Mandelbrot set Successor of Singular Cardinal Non-saturation Foundations Fast club Generalized Clubs Erdos-Hajnal graphs projective Boolean algebra Dushnik-Miller

# 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