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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

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