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### Recent blog posts

- A strong form of König’s lemma October 21, 2017
- 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

### Keywords

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

# 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