### 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

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