### Archives

### 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

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

# 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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