### 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

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

# 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