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The model theory of differential fields with finitely many commuting derivations

Published online by Cambridge University Press:  12 March 2014

Tracey McGrail
Tracey McGrail*
Affiliation:
Department of Mathematics, Marist College, Poughkeepsie, NY 12601, USA, E-mail: tracey.mcgrail@marist.edu
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Abstract

In this paper we set out the basic model theory of differential fields of characteristic 0, which have finitely many commuting derivations. We give axioms for the theory of differentially closed differential fields with m derivations and show that this theory is ω-stable, model complete, and quantifier-eliminable, and that it admits elimination of imaginaries. We give a characterization of forking and compute the rank of this theory to be ωm + 1.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 65 , Issue 2 , June 2000 , pp. 885 - 913
Copyright
Copyright © Association for Symbolic Logic 2000

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References

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