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The Ultrafilter Characterization of Huge Cardinals

Robert J. Mignone
Proceedings of the American Mathematical Society
Vol. 90, No. 4 (Apr., 1984), pp. 585-590
DOI: 10.2307/2045035
Stable URL: http://www.jstor.org/stable/2045035
Page Count: 6
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The Ultrafilter Characterization of Huge Cardinals
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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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