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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

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

# 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