### 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

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

# 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