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- The reflection principle $R_2$ May 20, 2016
- Prolific Souslin trees March 17, 2016
- 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

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

# 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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