On ultraproducts of Boolean algebras and irr

Saharon Shelah*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

§ 1. Consistent inequality [We prove the consistency of irr(∏ i<K Bi/D) < ∏i<K irr(B i)/D where D is an ultrafilter on K and each Bi is a Boolean algebra and irr(B) is the maximal size of irredundant subsets of a Boolean algebra B, see full definition in the text. This solves the last problem, 35, of this form from Monk's list of problems in [M2]. The solution applies to many other properties, e.g. Souslinity.] § 2. Consistency for small cardinals [We get similar results with K = א1 (easily we cannot have it for K = א0) and Boolean algebras Bi (i < K) of cardinality < ω1.] This article continues Magidor Shelah [MgSh 433] and Shelah Spinas [ShSi 677], but does not rely on them: see [M2] for the background.

Original languageEnglish
Pages (from-to)569-581
Number of pages13
JournalArchive for Mathematical Logic
Volume42
Issue number6
DOIs
StatePublished - Aug 2003

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