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Unions and the axiom of choice

✍ Scribed by Omar De la Cruz; Eric J. Hall; Paul Howard; Kyriakos Keremedis; Jean E. Rubin

Publisher
John Wiley and Sons
Year
2008
Tongue
English
Weight
176 KB
Volume
54
Category
Article
ISSN
0044-3050

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✦ Synopsis

Abstract

We study statements about countable and well‐ordered unions and their relation to each other and to countable and well‐ordered forms of the axiom of choice. Using WO as an abbreviation for β€œwell‐orderable”, here are two typical results: The assertion that every WO family of countable sets has a WO union does not imply that every countable family of WO sets has a WO union; the axiom of choice for WO families of WO sets does not imply that the countable union of countable sets is WO. (Β© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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