### 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

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

# 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