### 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

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

# 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