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Ultraproducts of finite sets

Published online by Cambridge University Press:  12 March 2014

H. Jerome Keisler
H. Jerome Keisler*
Affiliation:
University of Wisconsin
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Extract

It is shown in [1] that an ultraproduct of finite sets can be of arbitrarily large cardinality, but if it is infinite then it must have at least the power of the continuum. In this paper we shall take a closer look at the cardinality of ultraproducts of finite sets. Our results were announced without proof in [5]. A discussion of the cardinality of ultraproducts of infinite sets, and another theorem about ultraproducts of finite sets, can be found in [3].

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 32 , Issue 1 , June 1967 , pp. 47 - 57
Copyright
Copyright © Association for Symbolic Logic 1967

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References

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