### 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

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

# 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