### 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

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

# 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