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Unsupported Boolean algebras and forcing

✍ Scribed by Miloš S. Kurilić

Publisher: John Wiley and Sons
Year: 2004
Tongue: English
Weight: 179 KB
Volume: 50
Category: Article
ISSN: 0044-3050
DOI: 10.1002/malq.200410003

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✦ Synopsis

Abstract

If κ is an infinite cardinal, a complete Boolean algebra B is called κ‐supported if for each sequence 〈b~β~ : β < κ〉 of elements of B the equality $ \wedge$~α<κ~ $ \vee$~β>α~ b~β~ = $ \vee$ $ \wedge$~β∈A~ b~β~ holds. Combinatorial and forcing equivalents of this property are given and compared with the other forcing related properties of Boolean algebras (distributivity, caliber, etc.). The set of regular cardinals κ for which B is not κ‐supported is investigated. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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