Differential forms in the model theory of differential fields

Journal of Symbolic Logic 68 (3):923-945 (2003)
Abstract
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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