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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

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