Differential forms in the model theory of differential fields

Journal of Symbolic Logic 68 (3):923-945 (2003)
Fields of characteristic zero with several commuting derivations can be treated as fields equipped with a space of derivations that is closed under the Lie bracket. The existentially closed instances of such structures can then be given a coordinate-free characterization in terms of differential forms. The main tool for doing this is a generalization of the Frobenius Theorem of differential geometry
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DOI 10.2178/jsl/1058448448
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Generic Automorphisms of Fields.Angus Macintyre - 1997 - Annals of Pure and Applied Logic 88 (2):165-180.
Model Completion of Lie Differential Fields.Yoav Yaffe - 2001 - Annals of Pure and Applied Logic 107 (1-3):49-86.

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