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### Recent blog posts

- Genearlizations of Martin’s Axiom and the well-met condition January 11, 2015
- Many diamonds from just one January 6, 2015
- Happy new jewish year! September 24, 2014
- 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

### Keywords

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

# 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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