Fields with several commuting derivations

Abstract

For every natural number $m$, the existentially closed models of the theory of fields with $m$ commuting derivations can be given a first-order geometric characterization in several ways. In particular, the theory of these differential fields has a model-companion. The axioms are that certain differential varieties determined by certain ordinary varieties are nonempty. There is no restriction on the characteristic of the underlying field.

arXiv comment18 pages

Cited by in corpus (2)

• Contributions to the model theory of partial differential fields
• Geometric Axioms for Differentially Closed Fields with Several Commuting Derivations