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David Pierce (2003). Differential Forms in the Model Theory of Differential Fields.

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  1.  3
    Generic Automorphisms of Fields.Angus Macintyre - 1997 - Annals of Pure and Applied Logic 88 (2):165-180.
    It is shown that the theory of fields with an automorphism has a decidable model companion. Quantifier-elimination is established in a natural language. The theory is intimately connected to Ax's theory of pseudofinite fields, and analogues are obtained for most of Ax's classical results. Some indication is given of the connection to nonstandard Frobenius maps.
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    Model Completion of Lie Differential Fields.Yoav Yaffe - 2001 - Annals of Pure and Applied Logic 107 (1-3):49-86.
    We define a Lie differential field as a field of characteristic 0 with an action, as derivations on , of some given Lie algebra . We assume that is a finite-dimensional vector space over some sub-field given in advance. As an example take the field of rational functions on a smooth algebraic variety, with .For every simple extension of Lie differential fields we find a finite system of differential equations that characterizes it. We then define, using first-order conditions, a collection (...)
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