### 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

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

# 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