Differential forms in the model theory of differential fields


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Pierce D.

JOURNAL OF SYMBOLIC LOGIC, vol.68, no.3, pp.923-945, 2003 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 68 Issue: 3
  • Publication Date: 2003
  • Doi Number: 10.2178/jsl/1058448448
  • Title of Journal : JOURNAL OF SYMBOLIC LOGIC
  • Page Numbers: pp.923-945

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.