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- Prolific Souslin trees March 17, 2016
- Genearlizations 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
- Walk on countable ordinals: the characteristics December 1, 2013
- Polychromatic colorings November 26, 2013

### Keywords

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

# 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

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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