### Archives

### 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

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

# 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