Boolean algebras as unions of chains of subalgebras
type: Item
instance of: scholarly article
title: Boolean algebras as unions of chains of subalgebras
zbMATH Open document ID: 0358.06033
DOI: 10.1007/BF02485429
author: Sabine Koppelberg
published in: Algebra Universalis
publication date: 1977-01-01T00:00:00Z
review text: For every infinite Boolean algebra \(B\), \(\operatorname{cf} B\) (the cofinality of \(B\)) is defined to be the least infinite cardinal \(\kappa\) such that \(B\) is the union of a strictly ascending chain of subalgebras \(B_\alpha\), \(\alpha<\kappa\). It is proved that \(\operatorname{cf} B\leq 2^{\aleph_0}\) and \(\operatorname{cf} B=\aleph_1\) if \(B\) is \(\sigma\)-complete. Moreover, some classes of Boolean algebras are described such that \(\operatorname{cf} B=\aleph_0\), for each member of the classes. It seems to be unknown whether there is some \(B\) such that \(\operatorname{cf}B\geq \aleph_2\).
Mathematics Subject Classification ID: 06E05
zbMATH DE Number: 3557855
MaRDI profile type: Publication
cites work: Boolean algebras with ordered bases
cites work: Q4075092
full work available at URL: https://doi.org/10.1007/bf02485429
OpenAlex ID: W2086060552
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description: scientific article; zbMATH DE number 3557855