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Journal Article

# Shorter Notes: The Cardinality of Ultrapowers--An Example

Proceedings of the American Mathematical Society
Vol. 28, No. 1 (Apr., 1971), pp. 311-312
DOI: 10.2307/2037806
Stable URL: http://www.jstor.org/stable/2037806
Page Count: 2

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Topics: Cardinality, Ultrapowers, Ultraproducts, Mathematics

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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 $A^I$.