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### Recent blog posts

- Prikry forcing may add a Souslin tree June 12, 2016
- 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

### Keywords

Antichain Poset Shelah's Strong Hypothesis Prikry-type forcing Singular coﬁnality Non-saturation incompactness Diamond Singular cardinals combinatorics Microscopic Approach Cohen real Rock n' Roll approachability ideal stationary hitting Universal Sequences Minimal Walks Dushnik-Miller Absoluteness weak square S-Space Small forcing Hereditarily Lindelöf space P-Ideal Dichotomy Square-Brackets Partition Relations diamond star Reduced Power Knaster 05D10 OCA Ascent Path b-scale Successor of Regular Cardinal square Almost Souslin Rainbow sets Commutative cancellative semigroups 11P99 HOD Coherent tree stationary reflection tensor product graph projective Boolean algebra Parameterized proxy principle Forcing weak diamond Successor of Singular Cardinal Cardinal Invariants Rado's conjecture Cardinal function sap middle diamond Weakly compact cardinal Forcing Axioms Chang's conjecture Slim tree Fat stationary set Uniformization Partition Relations Constructible Universe Martin's Axiom Whitehead Problem Hedetniemi's conjecture Erdos-Hajnal graphs 05A17 Kurepa Hypothesis Axiom R Sakurai's Bell inequality Aronszajn tree Large Cardinals Erdos Cardinal Fast club polarized partition relation Generalized Clubs Singular Cofinality free Boolean algebra Jonsson cardinal Hindman's Theorem Chromatic number Foundations Selective Ultrafilter Almost-disjoint famiy Prevalent singular cardinals 20M14 ccc PFA Club Guessing Almost countably chromatic Singular Density Souslin Tree very good scale Mandelbrot set Ostaszewski square reflection principles Stevo Todorcevic L-space PFA(S)[S]

# 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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