### 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

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

# 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