An Invitation to Extension Domination

Abstract

Motivated by the theory of domination for types, we introduce a notion of domination for Keisler measures called extension domination. We argue that this variant of domination behaves similarly to its typesetting counterpart. We prove that extension domination extends domination for types and that it forms a preorder on the space of global Keisler measures. We then explore some basic properties related to this notion (e.g., approximations by formulas, closure under localizations, convex combinations). We also prove a few preservation theorems and provide some explicit examples.