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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

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

# 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