### 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

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

# Category Archives: Preprints

## A remark on Schimmerling’s question

Joint work with Ari Meir Brodsky. Abstract. Schimmerling asked whether $\square^*_\lambda$ together with GCH entails the existence of a $\lambda^+$-Souslin tree, for a singular cardinal $\lambda$. Here, we provide an affirmative answer under the additional assumption that there exists a … Continue reading

## 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