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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

### Keywords

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

Ace Billet Alan Mekler Albin L. Jones Alex Primavesi Alfred Tarski András Hajnal Benoit Mandelbrot Boban Velickovic Chen Meiri Chris Hadfield Ernest Schimmerling Fred Glavin Gabriel Belachsan Hiroshi Sakai Ilijas Farah Itay Neeman Jack Silver Jim Baumgartner John Krueger Judy Roitman Keith Devlin Menachem Magidor Mirna Dzamonja Moti Gitik Murray Bell Paul Erdős Paul Larson Richard Laver Ronald Jensen Saharon Shelah Sakaé Fuchino Stevo Todorcevic Teruyuki Yorioka Wacław Sierpiński

# 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