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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

PFA Cardinal Invariants Prevalent singular cardinals Almost Souslin P-Ideal Dichotomy Commutative cancellative semigroups Parameterized proxy principle Whitehead Problem Antichain Singular cardinals combinatorics Ostaszewski square Almost countably chromatic coloring number 11P99 Generalized Clubs Martin's Axiom weak diamond free Boolean algebra Fat stationary set Chromatic number Hedetniemi's conjecture Shelah's Strong Hypothesis square 05D10 Large Cardinals Jonsson cardinal Selective Ultrafilter Coherent tree Successor of Regular Cardinal Cardinal function sap reflection principles Minimal Walks Constructible Universe Uniformization Knaster Small forcing stationary reflection weak square S-Space Cohen real PFA(S)[S] projective Boolean algebra ccc Sakurai's Bell inequality Dushnik-Miller Slim tree Postprocessing function b-scale Weakly compact cardinal Rainbow sets xbox Souslin Tree 20M14 Singular coﬁnality Distributive tree Hereditarily Lindelöf space Successor of Singular Cardinal Rado's conjecture Fodor-type reflection Diamond Aronszajn tree very good scale Club Guessing Chang's conjecture Erdos-Hajnal graphs incompactness HOD middle diamond Axiom R Forcing tensor product graph Fast club 05A17 Rock n' Roll Reduced Power Foundations diamond star Prikry-type forcing Partition Relations Uniformly coherent Almost-disjoint famiy Stevo Todorcevic Absoluteness polarized partition relation Hindman's Theorem Singular Density Microscopic Approach Kurepa Hypothesis Poset Ascent Path Forcing Axioms Erdos Cardinal Nonspecial tree square principles approachability ideal Non-saturation Square-Brackets Partition Relations stationary hitting OCA L-space Universal Sequences Mandelbrot set

# 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
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## 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
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