How many Boolean algebras \({\mathcal P}(\mathbb{N})/{\mathcal I}\) are there?
type: Item
instance of: scholarly article
title: How many Boolean algebras \({\mathcal P}(\mathbb{N})/{\mathcal I}\) are there?
zbMATH Open document ID: 1025.03050
author: Ilijas Farah
published in: Illinois Journal of Mathematics
publication date: 2003-11-26T00:00:00Z
review text: The author considers the question in the title for ideals restricted to lie in one of several classes of ideals. Some main results are: (1) under CH, there are just two quotients using dense density ideals; (2) under CH, there are exactly six quotients using ideals associated with certain measures; (3) under CH, there is just one quotient using Louveau-Velickovic ideals; (4) in ZFC, there are at least 21 quotients associated with analytic \(P\)-ideals. In a note added in proof, the author states that M. R. Oliver in his UCLA PhD thesis completely took care of (4) by showing that there are continuum many such quotients. Some of the above results are proved by extending arguments of Just and Krawczyk. There are several other related results, in particular concerning automorphisms of quotients.
Mathematics Subject Classification ID: 03E50
Mathematics Subject Classification ID: 06E05
Mathematics Subject Classification ID: 03E05
zbMATH DE Number: 1952924
zbMATH Keywords: ideals
zbMATH Keywords: quotients
zbMATH Keywords: power set algebras
reviewed by: J. Donald Monk
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1952924