Model theory of partial differential fields: From commuting to noncommuting derivations

Abstract

McGrail (2000) has shown the existence of a model completion for the universal theory of fields on which a finite number of commuting derivations act and, independently, Yaffe (2001) has shown the existence of a model completion for the univeral theory of fields on which a fixed Lie algebra acts as derivations. We show how to derive the second result from the first.