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- 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

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

# 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