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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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The ultrafilter characterization of huge cardinals
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by Robert J. Mignone PDF
Proc. Amer. Math. Soc. 90 (1984), 585-590 Request permission

Abstract:

A huge cardinal can be characterized using ultrafilters. After an argument is made for a particular ultrafilter characterization, it is used to prove the existence of a measurable cardinal above the huge cardinal, and an ultrafilter over the set of all subsets of this measurable cardinal of size smaller than the huge cardinal. Finally, this last ultrafilter is disassembled intact by a process which often produces a different ultrafilter from the one started out with. An important point of this paper is given the existence of the particular ultrafilter characterization of a huge cardinal mentioned above these results are proved in Zermelo-Fraenkel set theory without the axiom of choice.
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Additional Information
  • © Copyright 1984 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 90 (1984), 585-590
  • MSC: Primary 03E55; Secondary 03E60
  • DOI: https://doi.org/10.1090/S0002-9939-1984-0733411-6
  • MathSciNet review: 733411