### Archives

### 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

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

# Tag Archives: Fat stationary set

## Distributive Aronszajn trees

Joint work with Ari Meir Brodsky. Abstract. Ben-David and Shelah proved that if $\lambda$ is a singular strong-limit cardinal and $2^\lambda=\lambda^+$, then $\square^*_\lambda$ entails the existence of a $\lambda$-distributive $\lambda^+$-Aronszajn tree. Here, it is proved that the same conclusion remains … Continue reading

## 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