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 | References | Similar Articles | Additional Information

Abstract: Assuming the consistency of huge cardinals, we prove that can carry an ultrafilter *D* such that has cardinality . (Hence *D* is not regular.) Similarly can carry an ultrafilter *D* such that has cardinality . (Hence *D* is not regular.)

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1979-0526312-2

Keywords:
Ultrafilter,
ultraproduct,
regular ultrafilter,
huge cardinals

Article copyright:
© Copyright 1979
American Mathematical Society