### 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

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

# 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