Stable forking and imaginaries

TL;DR

This paper establishes an equivalence between a theory having stable forking and its expansion with imaginaries also having stable forking, deepening understanding of stability properties in model theory.

Contribution

It proves that stable forking in a theory is equivalent to stable forking in its imaginary expansion, clarifying the relationship between these concepts.

Findings

Stable forking in a theory iff in its imaginary expansion

Deepens understanding of stability in model theory

Provides a key equivalence in forking behavior

Abstract

We prove that a theory $T$ has stable forking if and only if $T^\mathrm{eq}$ has stable forking.