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### 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

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

# Tag Archives: 03E57

## 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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