### 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

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

# 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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