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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
- Genearlizations 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

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

# 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