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### Recent blog posts

- Square principles April 19, 2014
- Partitioning the club guessing January 22, 2014
- Walk on countable ordinals: the characteristics December 1, 2013
- Polychromatic colorings November 26, 2013
- Universal binary sequences November 14, 2013
- Syndetic colorings with applications to S and L October 26, 2013
- Open coloring and the cardinal invariant $\mathfrak b$ October 8, 2013
- Gabriel Belachsan (14/5/1976 – 20/8/2013) August 20, 2013

### Keywords

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

# 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