Abstract
AbstractWe study a partial order on countably complete ultrafilters introduced by Ketonen [2] as a generalization of the Mitchell order. The following are our main results: the order is wellfounded; its linearity is equivalent to the Ultrapower Axiom, a principle introduced in the author’s dissertation [1]; finally, assuming the Ultrapower Axiom, the Ketonen order coincides with Lipschitz reducibility in the sense of generalized descriptive set theory.
Publisher
Cambridge University Press (CUP)
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1. Measurable cardinals and choiceless axioms;Annals of Pure and Applied Logic;2024-01