### 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

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

# 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