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

# 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