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### 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

Slim tree 11P99 Mandelbrot set Successor of Singular Cardinal square 20M14 Postprocessing function Aronszajn tree Kurepa Hypothesis Reduced Power Martin's Axiom reflection principles Coherent tree Erdos Cardinal Cohen real approachability ideal Fast club Parameterized proxy principle tensor product graph polarized partition relation Cardinal Invariants Nonspecial tree Partition Relations Chromatic number Souslin Tree Weakly compact cardinal Distributive tree Successor of Regular Cardinal Singular cardinals combinatorics Generalized Clubs P-Ideal Dichotomy square principles Minimal Walks Square-Brackets Partition Relations Singular coﬁnality Rado's conjecture Selective Ultrafilter Cardinal function Knaster Axiom R sap Forcing Prikry-type forcing Sakurai's Bell inequality stationary hitting 05A17 Erdos-Hajnal graphs Hindman's Theorem Foundations Hedetniemi's conjecture Uniformly coherent weak diamond Almost-disjoint famiy weak square Uniformization Fodor-type reflection Universal Sequences PFA(S)[S] Singular Density PFA Club Guessing xbox Stevo Todorcevic Shelah's Strong Hypothesis Antichain Rock n' Roll very good scale Ascent Path Microscopic Approach Jonsson cardinal Diamond L-space Fat stationary set Almost Souslin Poset Whitehead Problem 05D10 Forcing Axioms free Boolean algebra Ostaszewski square Rainbow sets Dushnik-Miller middle diamond Commutative cancellative semigroups Non-saturation Large Cardinals S-Space Constructible Universe projective Boolean algebra Small forcing diamond star Almost countably chromatic incompactness coloring number b-scale Hereditarily Lindelöf space HOD Prevalent singular cardinals ccc Absoluteness OCA stationary reflection Chang's conjecture

# Tag Archives: Forcing Axioms

## 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