Canonical quotients in model theory

TL;DR

This paper investigates canonical quotients in model theory, focusing on stable quotients, invariant types, and properties like WAP and tame quotients, extending existing concepts to continuous theories and analyzing their independence from model choices.

Contribution

It extends the modelling property to continuous theories and studies maximal WAP and tame quotients, showing their independence from the choice of monster model.

Findings

Maximal WAP and tame quotients are independent of the monster model used.

Extended the modelling property to continuous theories.

Analyzed $n$-dependence in hyperdefinable sets.

Abstract

We study canonical quotients in model theory, mainly stable quotients of type-definable groups and invariant types in NIP theories. We extend the modelling property to continuous theories and use it to study $n$-dependence in hyperdefinable sets. Furthermore, we study maximal WAP and tame quotients of $S_X(\mathfrak{C})$, where $\mathfrak{C}$ is a monster model of a complete theory $T$ and $X$ is an $\emptyset$-type-definable set and show that the Ellis groups of the maximal WAP quotient flow and the maximal tame quotient flow do not depend on the choice of the monster model $\mathfrak{C}$.