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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

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

# Tag Archives: super-Souslin tree

## 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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