### 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
- Genearlizations 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

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

# 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