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The cardinality of ultrapowers--an example


Author: Andrew Adler
Journal: Proc. Amer. Math. Soc. 28 (1971), 311-312
MSC: Primary 02.68
DOI: https://doi.org/10.1090/S0002-9939-1971-0280361-9
MathSciNet review: 0280361
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Abstract: Assume the axiom of measurable cardinals. If $ D$ is an $ \omega $-incomplete uniform ultrafilter on $ I$, and $ A$ is infinite, it is still not necessarily the case that $ {A^I}/D$ has the same cardinality as $ {A^I}$.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0280361-9
Keywords: Ultrapower, cardinality, measurable cardinal, regular ultrafilter
Article copyright: © Copyright 1971 American Mathematical Society

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