How large can a hereditarily separable or hereditarily Lindelöf space be?
type: Item
instance of: scholarly article
title: How large can a hereditarily separable or hereditarily Lindelöf space be?
zbMATH Open document ID: 0607.54002
DOI: 10.1007/BF02786567
author: István Juhász
author: S. Shelah
published in: Israel Journal of Mathematics
publication date: 1986-01-01T00:00:00Z
review text: Question: are there consistent examples of hereditarily separable spaces of size \(>2^{\omega_ 1}\) and of hereditarily Lindelöf spaces of weight \(>2^{\omega_ 1}?\) The answer given here is yes. Theorem. Let \(V\vDash GCH+\lambda\), \(\mu\) regular, \(\omega_ 1<\lambda <\mu\). Then there is a forcing extension of V which collapses no cardinals in which \(2^{\omega}=2^{\omega_ 1}=\lambda\) and there are a hereditarily separable space of size \(\mu\) and a hereditarily Lindelöf space of weight \(\mu\).
Mathematics Subject Classification ID: 54A25
zbMATH DE Number: 3982025
zbMATH Keywords: hereditarily separable spaces
zbMATH Keywords: hereditarily Lindelöf spaces
zbMATH Keywords: weight
reviewed by: Judith Roitman
MaRDI profile type: Publication
cites work: Q5547268
cites work: A consistency result concerning hereditarily α-Lindelöf spaces
cites work: Q4043743
cites work: Q3337413
cites work: Q3938195
cites work: Attaining the spread at cardinals of cofinality \(\omega\)
cites work: Attaining the spread at cardinals which are not strong limits
cites work: Easy S and L Groups
cites work: Forcing Positive Partition Relations
full work available at URL: https://doi.org/10.1007/bf02786567
OpenAlex ID: W1988868224
description: scientific article; zbMATH DE number 3982025