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- A strong form of König’s lemma October 21, 2017
- Prikry forcing may add a Souslin tree June 12, 2016
- The reflection principle $R_2$ May 20, 2016
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- Generalizations of Martin’s Axiom and the well-met condition January 11, 2015
- Many diamonds from just one January 6, 2015
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P-Ideal Dichotomy Partition Relations 20M14 Slim tree Nonspecial tree Stevo Todorcevic Cardinal Invariants Rainbow sets b-scale Cardinal function Fast club Almost countably chromatic 11P99 Constructible Universe Poset Minimal Walks Uniformization sap Uniformly coherent Axiom R Distributive tree Souslin Tree projective Boolean algebra Prikry-type forcing free Boolean algebra Erdos Cardinal Generalized Clubs Luzin set Whitehead Problem Foundations Mandelbrot set stationary hitting Hedetniemi's conjecture tensor product graph Kurepa Hypothesis Singular coﬁnality Large Cardinals polarized partition relation Prevalent singular cardinals Postprocessing function stationary reflection Jonsson cardinal Ostaszewski square Aronszajn tree Dushnik-Miller Coherent tree Square-Brackets Partition Relations very good scale Forcing Weakly compact cardinal super-Souslin tree Commutative cancellative semigroups Singular Density Singular cardinals combinatorics Martin's Axiom 05A17 Ascent Path Chang's conjecture Reduced Power PFA(S)[S] Fat stationary set Hindman's Theorem reflection principles Sakurai's Bell inequality Almost Souslin S-Space Successor of Regular Cardinal coloring number Universal Sequences weak diamond weak square ccc Forcing Axioms square principles Selective Ultrafilter Parameterized proxy principle OCA Club Guessing Hereditarily Lindelöf space PFA Diamond Absoluteness Non-saturation Microscopic Approach Chromatic number approachability ideal Erdos-Hajnal graphs xbox Small forcing Knaster HOD L-space square Antichain middle diamond Fodor-type reflection diamond star Almost-disjoint famiy Rock n' Roll Rado's conjecture incompactness Successor of Singular Cardinal Cohen real Shelah's Strong Hypothesis

# Tag Archives: OCA

## Open coloring and the cardinal invariant $\mathfrak b$

Nik Weaver asked for a direct proof of the fact that Todorcevic’s axiom implies the failure of CH fails. Here goes. Notation. For a set $X$, we write $[X]^2$ for the set of unordered pairs $\{ \{x,x’\}\mid x,x’\in X, x\neq … Continue reading