### 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

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

# 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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