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### 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

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

# 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

## The S-space problem, and the cardinal invariant $\mathfrak p$

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