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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

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

# 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