English

The Linearity of the Mitchell Order

Logic 2017-07-05 v2

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.

Keywords

Cite

@article{arxiv.1706.07141,
  title  = {The Linearity of the Mitchell Order},
  author = {Gabriel Goldberg},
  journal= {arXiv preprint arXiv:1706.07141},
  year   = {2017}
}
R2 v1 2026-06-22T20:25:58.175Z