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### Recent blog posts

- 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

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

# Tag Archives: Forcing Axioms

## 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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## Bell’s theorem on the cardinal invariant $\mathfrak p$

In this post, we shall provide a proof to a famous theorem of Murray Bell stating that $MA_\kappa(\text{the class of }\sigma\text{-centered posets})$ holds iff $\kappa<\mathfrak p$. We commence with defining the cardinal invariant $\mathfrak p$. For sets $A$ and $B$, … Continue reading