### 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

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

# 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