### 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

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

# Tag Archives: square principles

## 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

## ASL North American Meeting, March 2017

I gave a plenary talk at the 2017 ASL North American Meeting in Boise, March 2017. Talk Title: The current state of the Souslin problem. Abstract: Recall that the real line is that unique separable, dense linear ordering with no endpoints in … Continue reading