Model Theory of Differential Fields

1996 ◽  
pp. 38-113 ◽  
Author(s):  
David Marker
Keyword(s):  
Model Theory ◽  
Differential Fields

Differential forms in the model theory of differential fields

2003 ◽  
Vol 68 (3) ◽  
pp. 923-945 ◽  
Author(s):  
David Pierce
Keyword(s):  
Differential Geometry ◽  
Model Theory ◽  
Characteristic Zero ◽  
Differential Forms ◽  
Main Tool ◽  
Frobenius Theorem ◽  
Lie Bracket ◽  
Existentially Closed ◽  
Differential Fields

AbstractFields 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.

scholarly journals Imaginaries and invariant types in existentially closed valued differential fields

2019 ◽  
Vol 2019 (750) ◽  
pp. 157-196 ◽  
Author(s):  
Silvain Rideau
Keyword(s):  
Model Theory ◽  
Extension Property ◽  
Valued Fields ◽  
Invariant Extension ◽  
Open Questions ◽  
Existentially Closed ◽  
Differential Fields ◽  
Abstract Criterion

Abstract We answer three related open questions about the model theory of valued differential fields introduced by Scanlon. We show that they eliminate imaginaries in the geometric language introduced by Haskell, Hrushovski and Macpherson and that they have the invariant extension property. These two results follow from an abstract criterion for the density of definable types in enrichments of algebraically closed valued fields. Finally, we show that this theory is metastable.

The model theory ofm-ordered differential fields

2006 ◽  
Vol 52 (4) ◽  
pp. 331-339 ◽  
Author(s):  
Cédric Rivière
Keyword(s):  
Model Theory ◽  
Differential Fields

The model theory of differential fields with finitely many commuting derivations

2000 ◽  
Vol 65 (2) ◽  
pp. 885-913 ◽  
Author(s):  
Tracey McGrail
Keyword(s):  
Model Theory ◽  
Stable Model ◽  
Basic Model ◽  
Differential Fields

AbstractIn 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.

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