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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

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

# 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