### 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

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

# 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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