### Archives

### Recent blog posts

- More notions of forcing 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

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

# 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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