Submission date: 15 March 2011.

Abstract:

A geometric first-order axiomatization of differentially closed fields of characteristic zero with several commuting derivations, in the spirit of Pierce-Pillay, is formulated in terms of a relative notion of prolongation for Kolchin-closed sets.

Mathematics Subject Classification: 03C65, 12H05

Keywords and phrases: Differential Field, Prolongation, Model Theory

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