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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

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

# 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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