Keisler's order via Boolean ultrapowers

TL;DR

This paper characterizes Keisler's order using Boolean ultrapowers, expanding the 'separation of variables' framework, and identifies good ultrafilters as those capturing the maximum class, answering a long-standing question.

Contribution

It introduces a new Boolean ultrapower-based characterization of Keisler's order and identifies good ultrafilters as the ones corresponding to the maximum class.

Findings

Boolean ultrapowers characterize Keisler's order.

Good ultrafilters correspond to the maximum class in Keisler's order.

Answers a 1974 question by Benda about ultrafilters.

Abstract

In this paper, we provide a new characterization of Keisler's order in terms of saturation of Boolean ultrapowers. To do so, we apply and expand the framework of 'separation of variables' recently developed by Malliaris and Shelah. We also show that good ultrafilters on Boolean algebras are precisely the ones which capture the maximum class in Keisler's order, answering a question posed by Benda in 1974.