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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

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

# 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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