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### 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

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

# 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