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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

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

# 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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