### Archives

### Recent blog posts

- A strong form of König’s lemma October 21, 2017
- 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

### Keywords

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

# 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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