Remark on the altitude of Boolean algebras
type: Item
instance of: scholarly article
title: Remark on the altitude of Boolean algebras
zbMATH Open document ID: 0656.06014
DOI: 10.1007/BF01229978
author: Winfried Just
published in: Algebra Universalis
publication date: 1988-01-01T00:00:00Z
review text: The altitude of a BA A is the least infinite cardinal \(\lambda\) such that there is an ultrafilter F on A which is the union of a strictly increasing sequence of type \(\lambda\) of filters on A. This notion is closely related to the cofinality of A, studied by S. Koppelberg. It is a big open problem whether the altitude is always at most \(\omega_ 1\); it is easy to see that it is always at most \(2^{\omega}\). Here the author shows that it is consistent that CH fails and still every BA has altitude at most \(\omega_ 1\).
Mathematics Subject Classification ID: 06E05
Mathematics Subject Classification ID: 03E35
zbMATH DE Number: 4070977
zbMATH Keywords: altitude
zbMATH Keywords: ultrafilter
zbMATH Keywords: cofinality
zbMATH Keywords: CH
reviewed by: J. Donald Monk
MaRDI profile type: Publication
cites work: The consistency of \(``\neg CH+pa\leq \omega_ 1''\)
cites work: Boolean algebras as unions of chains of subalgebras
cites work: Some questions about Boolean algebras
description: scientific article; zbMATH DE number 4070977