### 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
- Generalizations 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

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

# 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
4 Comments

## 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, February 2007

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
8 Comments