Model theory, differential algebra and functional transcendence

TL;DR

This paper explores the application of geometric model theory to differential algebra, focusing on functional transcendence and the C$_2$-property within differentially closed fields, providing tools for recent significant proofs.

Contribution

It introduces methods from geometric model theory tailored to differential algebra, elucidating their role in proving functional transcendence results and the C$_2$-property.

Findings

Development of geometric model theory tools for differential fields

Explanation of the C$_2$-property in the context of differential algebra

Application of these methods to recent proofs of functional transcendence

Abstract

The goal of this text is to exhibit some of the ideas and methods from geometric model theory, translated to the particular context of differentially closed fields, exhibiting in a more or less self-contained way the tools needed for the recent proof of Freitag, Jaoui and Moosa on functional transcendence and their so-called C$_2$-property, which serves as a leitmotif for the presentation.