### 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

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

# Tag Archives: Uniformly coherent

## 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