Algebro-geometric axioms for DCF$_{0,m}$

TL;DR

This paper provides an algebro-geometric first-order axiomatization of the theory of differentially closed fields with multiple derivations, extending classical geometric axioms to a more complex setting.

Contribution

It introduces a novel algebro-geometric axiomatization for DCF$_{0,m}$, generalizing classical axioms from the single-derivation case to multiple derivations.

Findings

First-order axiomatization of DCF$_{0,m}$ using algebraic geometry

Extension of classical geometric axioms to multiple derivations

Framework for analyzing differential fields with several derivations

Abstract

We give an algebro-geometric first-order axiomatization of DCF$_{0,m}$ (the theory of differentially closed fields of characteristic zero with m commuting derivations) in the spirit of the classical geometric axioms of DCF$_0$.