Karp height of models of stable theories

TL;DR

This paper presents a trichotomy theorem for countable, stable, unsuperstable theories, introducing the concept of regular ideals and analyzing minimal types within this framework.

Contribution

It introduces the notion of regular ideals of formulas and studies minimal types, advancing the understanding of stable, unsuperstable theories.

Findings

Establishes a trichotomy theorem for certain theories

Develops the concept of regular ideals of formulas

Analyzes minimal types with respect to these ideals

Abstract

A trichotomy theorem for countable, stable, unsuperstable theories is offered. We develop the notion of a `regular ideal' of formulas and study types that are minimal with respect to such an ideal.