### 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

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

# 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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