### 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

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

# 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

## 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