On the model companion of partial differential fields with an automorphism

TL;DR

This paper proves the existence of a model companion for partial differential fields with an automorphism, explores its model theoretic properties, and demonstrates it satisfies the Zilber dichotomy for finite dimensional minimal types.

Contribution

It establishes the model companion for these fields and analyzes its fundamental model theoretic characteristics, including the Zilber dichotomy.

Findings

Existence of a model companion for partial differential fields with automorphism

Basic model theoretic properties established

Satisfies the Zilber dichotomy for finite dimensional minimal types

Abstract

We prove that the class of partial differential fields of characteristic zero with an automorphism has a model companion. We then establish the basic model theoretic properties of this theory and prove that it satisfies the Zilber dichotomy for finite dimensional minimal types.