We 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.

中文翻译：

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基托宁令

我们研究了 Ketonen [2] 引入的可数完全超滤器的偏阶，作为 Mitchell 阶的推广。以下是我们的主要结果： 订单有根据；其线性度相当于作者论文[1]中介绍的原理Ultrapower Axiom；最后，假设 Ultrapower 公理，Ketonen 阶与广义描述集合论意义上的 Lipschitz 可约性一致。