### 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

Non-saturation Diamond Successor of Regular Cardinal diamond star Knaster Coherent tree Hedetniemi's conjecture b-scale Constructible Universe Selective Ultrafilter stationary reflection Singular cardinals combinatorics Almost Souslin weak square Reduced Power 11P99 Nonspecial tree Ascent Path Ostaszewski square Generalized Clubs Postprocessing function Uniformly coherent Fast club P-Ideal Dichotomy PFA Weakly compact cardinal square principles Prikry-type forcing square Forcing Forcing Axioms Rainbow sets tensor product graph Small forcing approachability ideal coloring number Whitehead Problem Prevalent singular cardinals Antichain Aronszajn tree Parameterized proxy principle 05A17 20M14 weak diamond Erdos Cardinal Erdos-Hajnal graphs OCA Successor of Singular Cardinal Almost-disjoint famiy sap Kurepa Hypothesis Sakurai's Bell inequality 05D10 Microscopic Approach Universal Sequences middle diamond Cohen real Cardinal function Fodor-type reflection Luzin set Cardinal Invariants Commutative cancellative semigroups Chromatic number Souslin Tree Stevo Todorcevic Foundations Distributive tree Fat stationary set Uniformization Club Guessing Martin's Axiom Axiom R Slim tree Shelah's Strong Hypothesis Singular coﬁnality free Boolean algebra ccc polarized partition relation projective Boolean algebra Square-Brackets Partition Relations Almost countably chromatic incompactness very good scale Hindman's Theorem L-space Absoluteness Rock n' Roll PFA(S)[S] HOD Jonsson cardinal Minimal Walks reflection principles Mandelbrot set Dushnik-Miller S-Space Large Cardinals stationary hitting Rado's conjecture Hereditarily Lindelöf space Poset Singular Density Partition Relations xbox Chang's conjecture

# Category Archives: Preprints

## 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

## More notions of forcing add a Souslin tree

Joint work with Ari Meir Brodsky. Abstract. An $\aleph_1$-Souslin tree is a complicated combinatorial object whose existence cannot be decided on the grounds of ZFC alone. But 15 years after Tennenbaum and independently Jech devised notions of forcing for introducing … Continue reading