On pp elimination and stability in a continuous setting

TL;DR

This paper extends the concept of pp elimination to continuous logic settings involving abelian structures with homomorphisms to compact groups, demonstrating the stability of their theories.

Contribution

It generalizes pp elimination to a continuous logic framework for abelian structures with compact group homomorphisms, establishing their stability.

Findings

Continuous logic theory of such structures is stable

Generalization of pp elimination to a new setting

Framework for analyzing abelian structures with compact group homomorphisms

Abstract

We generalize pp elimination for modules, or more generally abelian structures, to a continuous logic environment where the abelian structure is equipped with a homomorphism to a compact (Hausdorff) group. We conclude that the continuous logic theory of such a structure is stable.