### Archives

### Recent blog posts

- 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
- Syndetic colorings with applications to S and L October 26, 2013
- Open coloring and the cardinal invariant $\mathfrak b$ October 8, 2013

### Keywords

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

# 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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