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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

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

# 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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