### 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

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

# 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