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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

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

# 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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