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

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

# 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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