The structure of the Mitchell order - II

TL;DR

This paper explores the structure of the Mitchell order on normal measures, demonstrating that any well-founded order can be realized on a measurable cardinal under certain large cardinal assumptions.

Contribution

It shows that every well-founded order can be represented as the Mitchell order on a measurable cardinal, given specific large cardinal hypotheses.

Findings

Any well-founded order can be realized as a Mitchell order.

The realization depends on large cardinal assumptions.

The work advances understanding of the Mitchell order's possible structures.

Abstract

We address the question regarding the structure of the Mitchell order on normal measures. We show that every well founded order can be realized as the Mitchell order on a measurable cardinal $\kappa$ from some large cardinal assumption.