Interpretations and differential Galois extensions

TL;DR

This paper provides model theoretic proofs for the existence and uniqueness of differential Galois extensions without new constants, for logarithmic differential equations over fields with possibly non-algebraically closed constants.

Contribution

It offers new model theoretic approaches to differential Galois theory, extending results to cases with non-algebraically closed constant fields.

Findings

Existence of differential Galois extensions under various assumptions.

Uniqueness of these extensions in the specified setting.

Extension of classical results to broader constant field contexts.

Abstract

We give model theoretic accounts and proofs of the existence and uniqueness of differential Galois extensions with no new constants, for logarithmic differential equations over a differential field K, when the field C of constants of K is not necessarily algebraically closed, under a variety of assumptions on C and K.