### 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
- 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

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

# 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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