Stable theories and representation over sets

TL;DR

This paper investigates the representation property over sets, showing it characterizes stable theories and providing stronger results for omega-stable theories.

Contribution

It establishes that the class of theories with models representable over sets precisely corresponds to stable theories, extending to omega-stable theories.

Findings

Representation property characterizes stable theories

Models of omega-stable theories have stronger representation results

The class of representable theories equals the class of stable theories

Abstract

In this paper we explore the representation property over sets. This property generalizes constructibility, however is weak enough to enable us to prove that the class of theories $T$ whose models are representable is exactly the class of stable theories. Stronger results are given for omega-stable.