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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

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

# 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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