Journal of Symbolic Logic

Differential forms in the model theory of differential fields

David Pierce

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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.

Article information

Source
J. Symbolic Logic, Volume 68, Issue 3 (2003), 923- 945.

Dates
First available in Project Euclid: 17 July 2003

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1058448448

Digital Object Identifier
doi:10.2178/jsl/1058448448

Mathematical Reviews number (MathSciNet)
MR2004h:03080

Zentralblatt MATH identifier
1060.03055

Subjects
Primary: 03C60: Model-theoretic algebra [See also 08C10, 12Lxx, 13L05]
Secondary: 03C10: Quantifier elimination, model completeness and related topics 12H05: Differential algebra [See also 13Nxx] 12L12: Model theory [See also 03C60] 13Nxx: Differential algebra [See also 12H05, 14F10]

Citation

Pierce, David. Differential forms in the model theory of differential fields. J. Symbolic Logic 68 (2003), no. 3, 923-- 945. doi:10.2178/jsl/1058448448. https://projecteuclid.org/euclid.jsl/1058448448


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