### 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

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

# Tag Archives: Hereditarily Lindelöf space

## The S-space problem, and the cardinal invariant $\mathfrak p$

Recall that an $S$-space is a regular hereditarily separable topological space which is not hereditarily Lindelöf. Do they exist? Consistently, yes. However, Szentmiklóssy proved that compact $S$-spaces do not exist, assuming Martin’s Axiom. Pushing this further, Todorcevic later proved that … Continue reading

Posted in Blog, Expository, Open Problems
Tagged Hereditarily Lindelöf space, P-Ideal Dichotomy, PFA(S)[S], S-Space
4 Comments

## 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

## Workshop on Set Theory and its Applications

These are the slides of a talk given at the Workshop on Set Theory and its Applications workshop (Weizmann Institute, February 19, 2007). Talk Title: Nets of spaces having singular density Abstract: The weight of a topological space X is the … 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
Leave a comment