### 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

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