### Archives

### Recent blog posts

- A strong form of König’s lemma October 21, 2017
- 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

### Keywords

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