| MODEL THEORY OF PARTIAL DIFFERENTIAL FIELDS: FROM COMMUTING TO NONCOMMUTING DERIVATIONS (2008) | |||||||||||||||
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| Abstract. McGrail [3] 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 [7] 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. 1. Introduction. In [3], McGrail gives axioms for the model completion of the universal theory of fields of characteristic zero with several commuting derivations. Independently, Yaffe [7] gave axioms for the model completion of the universal theory of a more general class of fields: LDF0, the universal theory of fields of characteristic zero | |||||||||||||||
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