### 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

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

# Tag Archives: Distributive 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