### 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

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

# Tag Archives: Fat stationary set

## Chain conditions of products, and weakly compact cardinals

Abstract. The history of productivity of the $\kappa$-chain condition in partial orders, topological spaces, or Boolean algebras is surveyed, and its connection to the set-theoretic notion of a weakly compact cardinal is highlighted. Then, it is proved that for every … Continue reading

Posted in Partition Relations, Publications
Tagged Aronszajn tree, ccc, Fat stationary set, Minimal Walks, square, Weakly compact cardinal
2 Comments

## The Ostaszewski square, and homogeneous Souslin trees

Abstract: Assume GCH and let $\lambda$ denote an uncountable cardinal. We prove that if $\square_\lambda$ holds, then this may be witnessed by a coherent sequence $\left\langle C_\alpha \mid \alpha<\lambda^+\right\rangle$ with the following remarkable guessing property: For every sequence $\langle A_i\mid i<\lambda\rangle$ … Continue reading

Posted in Publications, Souslin Hypothesis, Squares and Diamonds
Tagged 03E05, 03E35, Club Guessing, Fat stationary set, Ostaszewski square, Souslin Tree
5 Comments