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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

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

# 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