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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

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

# 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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