### 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

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

# 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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