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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

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

# 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