### 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
- 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

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

# Tag Archives: Cardinal Invariants

## 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

## Infinite Combinatorial Topology

Back in 2005, as a master student, I attended a course by Boaz Tsaban, entitled “Infinite Combinatorial Topology”. A friend and I decided to produce lecture notes, but in a somewhat loose sense, that is: we sometimes omit material given … Continue reading

Posted in Notes
Tagged b-scale, Cardinal function, Cardinal Invariants, Hereditarily Lindelöf space
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