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.
Citation
David Pierce. "Differential forms in the model theory of differential fields." J. Symbolic Logic 68 (3) 923 - 945, September 2003. https://doi.org/10.2178/jsl/1058448448
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