### 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

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

# 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