### 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

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

# Tag Archives: Cardinal function

## On topological spaces of singular density and minimal weight

Abstract: We introduce a weakening of the Generalized Continuum Hypothesis, which we will refer to as the Prevalent Singular cardinals Hypothesis (PSH), and show it implies that every topological space of density and weight $\aleph_{\omega_1}$ is not hereditarily Lindelöf. The assumption … 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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