Superstable theories and representation

TL;DR

This paper characterizes superstable theories using an external property called representation, extending previous characterizations for stable and aleph_0-stable theories, and providing a comprehensive understanding of their complexity.

Contribution

It offers a complete characterization of superstable theories through the concept of representation, broadening the understanding of their structural properties.

Findings

Superstable theories are characterized by a specific external property called representation.

The paper extends previous characterizations from stable and aleph_0-stable theories to superstable theories.

Provides a framework to view superstable theories as 'not very complicated' in terms of representation.

Abstract

In this paper we give characterizations of the super-stable theories, in terms of an external property called representation. In the sense of the representation property, the mentioned class of first-order theories can be regarded as "not very complicated". This was done for "stable" and for "aleph_0-stable". Here we give a complete answer for "superstable".