On Model Complete Differential Fields
نویسنده
چکیده
We develop a geometric approach to definable sets in differentially closed fields, with emphasis on the question of orthogonality to a given strongly minimal set. Equivalently, within a family of ordinary differential equations, we consider those equations that can be transformed, by differential-algebraic transformations, so as to yield solutions of a given fixed first-order ODE X. We show that this sub-family is usually definable (in particular if X lives on a curve of positive genus). As a corollary, we show the existence of many model-complete, superstable theories of differential fields.
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