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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

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

# Tag Archives: Knaster

## c.c.c. vs. the Knaster property

After my previous post on Mekler’s characterization of c.c.c. notions of forcing, Sam, Mike and myself discussed the value of it . We noticed that a prevalent verification of the c.c.c. goes like this: given an uncountable set of conditions, … Continue reading