The Linearity of the Mitchell Order

Gabriel Goldberg

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arXiv · 1706.07141

The Linearity of the Mitchell Order

Gabriel Goldberg

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Abstract

We show from a weak comparison principle (the Ultrapower Axiom) that the Mitchell order is linear on certain kinds of ultrafilters: normal ultrafilters, Dodd solid ultrafilters, and assuming GCH, generalized normal ultrafilters. In the process we prove a generalization of Solovay's lemma to singular cardinals.

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BibTeX RIS

Gabriel Goldberg. 2017-06-21. The Linearity of the Mitchell Order. https://arxiv.org/abs/1706.07141

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