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Unions of well-ordered sets

Part of: Set theory

Published online by Cambridge University Press:  09 April 2009

Paul Howard
Paul Howard
Affiliation:
Eastern Michigan University, Ypsilanti, MI 48197, USA
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Abstract

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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.

Keywords

axiom of choicecountable union theoremwell-ordered set.

MSC classification

Secondary: 03E35: Consistency and independence results 03E25: Axiom of choice and related propositions
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 56 , Issue 1 , February 1994 , pp. 117 - 124
Copyright
Copyright © Australian Mathematical Society 1994

References

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