### 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
- 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

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

# 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