### 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

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

# Tag Archives: Nonspecial tree

## 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