The Linearity of the Mitchell Order

DOI10.1142/S0219061318500058arXiv1706.07141WikidataQ130104051 ScholiaQ130104051MaRDI QIDQ6288158

Publication date: 21 June 2017

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.

Mathematics Subject Classification ID

Inner models, including constructibility, ordinal definability, and core models (03E45) Large cardinals (03E55)

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