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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

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

# 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