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### 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
- Genearlizations 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

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

# 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
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## 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
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