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- 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

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

# 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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