On model complete differential fields

Hrushovski, E.; Itai, M.

doi:10.1090/S0002-9947-03-03264-1

On model complete differential fields
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by E. Hrushovski and M. Itai PDF

Trans. Amer. Math. Soc. 355 (2003), 4267-4296 Request permission

Abstract:

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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