### 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

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

# 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