### Archives

### Recent blog posts

- A strong form of König’s lemma October 21, 2017
- 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

### Keywords

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