On tightly \(\kappa \)-filtered Boolean algebras.
type: Item
instance of: scholarly article
title: On tightly \(\kappa \)-filtered Boolean algebras.
zbMATH Open document ID: 1063.03036
author: Stefan Geschke
published in: Algebra Universalis
publication date: 2005-04-19T00:00:00Z
review text: In the paper the concept of tight \(\kappa \)-filteredness of a Boolean algebra for infinite regular cardinals \(\kappa \) is introduced and studied. Characterizations of tightly \(\kappa \)-filtered Boolean algebras which generalize the internal characterizations of projectivity are given. It is shown that for each \(\kappa \) there is an rc-filtered Boolean algebra that is not tightly \(\kappa \)-filtered. This generalizes a result of E. V. Ščepin. It is proved that no complete Boolean algebra of size larger than \(\aleph _{2}\) is tightly \(\aleph _{1}\)-filtered.
reviewed by: Radomír Halaš
Mathematics Subject Classification ID: 03E35
Mathematics Subject Classification ID: 03E05
Mathematics Subject Classification ID: 06E05
zbMATH DE Number: 2158767
zbMATH Keywords: projective Boolean algebra
zbMATH Keywords: weak Freese-Nation property
zbMATH Keywords: \(\sigma \)-filtered
MaRDI profile type: Publication
full work available at URL: s00012-002-8176-1
OpenAlex ID: W2013024255
DOI: 10.1007/S00012-002-8176-1
description: scientific article; zbMATH DE number 2158767