### 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

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

# 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