### Archives

### 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

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

# 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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