A geometric model of an arbitrary differentially closed field of characteristic zero

TL;DR

This paper presents a geometric construction of arbitrary differentially closed fields of characteristic zero using Nash function fields, providing new insights into their structure and properties.

Contribution

It introduces an elementary geometric method to construct differentially closed fields and characterizes Archimedean ordered differentially closed fields via Nash functions.

Findings

Constructed arbitrary differentially closed fields using Nash functions.

Provided a universal differential extension of a differential field.

Characterized Archimedean ordered differentially closed fields in terms of Nash functions.

Abstract

We give an elementary construction of an arbitrary differentially closed field and of a universal differential extension of a differential field in terms of Nash function fields. We also give a characterization of any Archimedean ordered differentially closed field in terms of Nash functions.