J Austral Math Soc Ser A 56 pp117--124, 1994.

Unions of Well-Ordered Sets

Paul Howard

Abstract

In Zermelo-Fraenkel set theory weakened to permit the existence of atoms and without the axiom of choice we investigate the deductive strength of five statements which make assertions about the cardinality of the union of a well-ordered collection of sets. All five of the statements considered are consequences of the axiom of choice.

1991 AMS Subject Classification: 03E35, 03E25, 04A25

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Authors

Paul Howard

Eastern Michigan University, Ypsilanti, MI 48197, USA.