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### Recent blog posts

- 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

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

# 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