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On generic extensions without the axiom of choice1

Published online by Cambridge University Press:  12 March 2014

G. P. Monro
G. P. Monro*
Affiliation:
University of Sydney, Sydney, NSW 2006, Australia
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Abstract

Let ZF denote Zermelo-Fraenkel set theory (without the axiom of choice), and let M be a countable transitive model of ZF. The method of forcing extends M to another model M[G] of ZF (a “generic extension”). If the axiom of choice holds in M it also holds in M[G], that is, the axiom of choice is preserved by generic extensions. We show that this is not true for many weak forms of the axiom of choice, and we derive an application to Boolean toposes.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 48 , Issue 1 , March 1983 , pp. 39 - 52
Copyright
Copyright © Association for Symbolic Logic 1983

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Footnotes

1

While the work for this paper was done the author held a Fellowship at the University of Heidelberg from the Alexander von Humboldt Foundation of West Germany.

References

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