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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

On the existence of nonregular ultrafilters and the cardinality of ultrapowers


Author: Menachem Magidor
Journal: Trans. Amer. Math. Soc. 249 (1979), 97-111
MSC: Primary 03E05; Secondary 03E35, 03E55
MathSciNet review: 526312
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Abstract: Assuming the consistency of huge cardinals, we prove that $ {\omega _3}$ can carry an ultrafilter D such that $ {\omega _1}^{{\omega _3}}/D$ has cardinality $ {\omega _3}$. (Hence D is not $ ({\omega _3},\,{\omega _1})$ regular.) Similarly $ {\omega _2}$ can carry an ultrafilter D such that $ {\omega ^{{\omega _2}}}/D$ has cardinality $ {\omega _2}$. (Hence D is not $ ({\omega _2},\,\omega )$ regular.)


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1979-0526312-2
PII: S 0002-9947(1979)0526312-2
Keywords: Ultrafilter, ultraproduct, regular ultrafilter, huge cardinals
Article copyright: © Copyright 1979 American Mathematical Society