Quotients of Boolean algebras and regular subalgebras
type: Item
instance of: scholarly article
title: Quotients of Boolean algebras and regular subalgebras
zbMATH Open document ID: 1196.03065
author: T. Pazák
author: Bohuslav Balcar
published in: Archive for Mathematical Logic
publication date: 2010-04-15T00:00:00Z
review text: The main theorem is that in any generic extension of \(M\) containing a new real there is an almost disjoint refinement of \([\omega]^\omega\) (in the \(M\) sense). This is applied to \({\mathcal P}(\omega)\)/fin to obtain information about the cardinal functions \(\mathfrak b\) and \(\mathfrak h\), using the notion of a splitting real. The minimal ideal \(I\) such that there is a regular embedding of \({\mathcal P}(\omega)\)/fin (in the sense of \(M\)) into \(({\mathcal P}(\omega)/\text{fin})/I\) (in the sense of \(M[G]\)) is investigated.
Mathematics Subject Classification ID: 03E40
Mathematics Subject Classification ID: 03E17
Mathematics Subject Classification ID: 06E05
zbMATH DE Number: 5693390
zbMATH Keywords: regular embedding
zbMATH Keywords: \({\mathcal P}(\omega)\)/fin
zbMATH Keywords: splitting real
reviewed by: J. Donald Monk
MaRDI profile type: Publication
full work available at URL: s00153-010-0174-y
OpenAlex ID: W2062180828
cites work: Q4513440
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DOI: 10.1007/S00153-010-0174-Y
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description: scientific article; zbMATH DE number 5693390