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Some definitions of finiteness

Published online by Cambridge University Press:  17 April 2009

J. L. Hickman
J. L. Hickman
Affiliation:
Flinders University, Bedford Park, South Australia.
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Abstract

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Since Paul J. Cohen's 1963 result, it has been possible to investigate the consequences of the axioms of Zermelo-Fraenkel set theory without the Axiom of Choice. In this paper we examine the relative strengths of a number of finiteness criteria against the background of ZF set theory without AC.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 5 , Issue 3 , December 1971 , pp. 321 - 330
Copyright
Copyright © Australian Mathematical Society 1971

References

[1]Cohen, Paul J., Set theory and the continuum hypothesis (Benjamin, New York, Amsterdam, 1966).Google Scholar
[2]Rosser, J. Barkley, Simplified independence proofs (Academic Press, New York, London, 1969).Google Scholar
[3]Tarski, Alfred, “Sur les ensembles finis”, Fund. Math. 6 (1924), 45–95.CrossRefGoogle Scholar