On the Consistency Strength of Irregular Ultra lters
نویسندگان
چکیده
The proof of the consistency of the existence of irregular ultra lters requires large cardinals. Foreman, Magidor, and Shelah forced the existence of a fully irregular ultra lter on a successor cardinal from a huge cardinal. That some large cardinal strength is necessary was shown by Ketonen (0) and Donder, Jensen, and Koppelberg (a measurable cardinal). We considerably improve this lower bound to show that (under some cardinal arithmetic restrictions), in fact, the existence of a model for a strong cardinal can be deduced:
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