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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

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

# 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