### Archives

### 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
- Genearlizations 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

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

# 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