### 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

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

# 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
8 Comments