Classification theory for theories with NIP - a modest beginning

TL;DR

This paper explores the classification theory for NIP theories, aiming to establish foundational results similar to those known for stable and simple theories, thereby advancing understanding of NIP model theory.

Contribution

It initiates the development of a classification framework for NIP theories, addressing foundational properties and laying groundwork for further research.

Findings

Identifies key properties of NIP theories

Establishes initial classification results

Suggests parallels with stable and simple theories

Abstract

A relevant thesis is that for the family of complete first order theories with NIP (i.e. without the independence property) there is a substantial theory, like the family of stable (and the family of simple) first order theories. We examine some properties.