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- Prikry forcing may add a Souslin tree June 12, 2016
- The reflection principle $R_2$ May 20, 2016
- Prolific Souslin trees March 17, 2016
- Generalizations of Martin’s Axiom and the well-met condition January 11, 2015
- Many diamonds from just one January 6, 2015
- Happy new jewish year! September 24, 2014
- Square principles April 19, 2014
- Partitioning the club guessing January 22, 2014

### Keywords

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

# 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