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### 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

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

# 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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