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### 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

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

# 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