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### Recent blog posts

- 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
- Syndetic colorings with applications to S and L October 26, 2013
- Open coloring and the cardinal invariant $\mathfrak b$ October 8, 2013

### Keywords

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