Unions and the axiom of choice

Mathematical Logic Quarterly 54 (6):652-665 (2008)

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 “well-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

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References found in this work

[Omnibus Review].Thomas Jech - 1992 - Journal of Symbolic Logic 57 (1):261-262.
Consequences of the Axiom of Choice.Paul Howard & Jean E. Rubin - 2005 - Bulletin of Symbolic Logic 11 (1):61-63.

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