### 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

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

# 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