### 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

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

# 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

## A forcing axiom deciding the generalized Souslin Hypothesis

Joint work with Chris Lambie-Hanson. Abstract. We derive a forcing axiom from the conjunction of square and diamond, and present a few applications, primary among them being the existence of super-Souslin trees. It follows that for every uncountable cardinal $\lambda$, … Continue reading

Posted in Preprints, Souslin Hypothesis
Tagged 03E05, 03E35, 03E57, Diamond, Forcing Axioms, Souslin Tree, square, super-Souslin tree
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## 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