The cardinality of ultrapowers—an example
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- by Andrew Adler
- Proc. Amer. Math. Soc. 28 (1971), 311-312
- DOI: https://doi.org/10.1090/S0002-9939-1971-0280361-9
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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 ${A^I}$.References
- C. C. Chang, Ultraproducts and other methods of constructing models, Sets, Models and Recursion Theory (Proc. Summer School Math. Logic and Tenth Logic Colloq., Leicester, 1965) North-Holland, Amsterdam, 1967, pp. 85–121. MR 0218223
- T. Frayne, A. C. Morel, and D. S. Scott, Reduced direct products, Fund. Math. 51 (1962/63), 195–228. MR 142459, DOI 10.4064/fm-51-3-195-228
- H. Jerome Keisler, A survey of ultraproducts, Logic, Methodology and Philos. Sci. (Proc. 1964 Internat. Congr.), North-Holland, Amsterdam, 1965, pp. 112–126. MR 0205852
- Simon Kochen, Ultraproducts in the theory of models, Ann. of Math. (2) 74 (1961), 221–261. MR 138548, DOI 10.2307/1970235
Bibliographic Information
- © Copyright 1971 American Mathematical Society
- 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