The group configuration theorem for generically stable types

TL;DR

This paper extends Hrushovski's group configuration theorem to include generically stable types, removing the need for the ambient theory to be tame, thus broadening its applicability in model theory.

Contribution

It generalizes the group configuration theorem to generically stable types without requiring the ambient theory to be tame.

Findings

Successfully extended the theorem to a broader class of types

Maintained the proof structure from the stable context

Enhanced understanding of generically stable types in model theory

Abstract

We generalize Hrushovski's group configuration theorem to the case where the type of the configuration is generically stable, without assuming tameness of the ambient theory. The properties of generically stable types, which we recall in the first section, enable us to adapt the proof known in the stable context.