### 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

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

# Category Archives: Preprints

## 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

## The eightfold way

Joint work with James Cummings, Sy-David Friedman, Menachem Magidor, and Dima Sinapova. Abstract. Three central combinatorial properties in set theory are the tree property, the approachability property and stationary reflection. We prove the mutual independence of these properties by showing … Continue reading