The Linearity of the Mitchell Order

2017/06/21 by Goldberg, Gabriel
#FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1706.07141

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.

Related

• The Seed Order
• The seed order
• Compactness and Comparison
• A note on the Ketonen order and Lipschitz reducibility between ultrafilters
• The combinatorics of reasonable ultrafilters