On model complete differential fields |
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| Authors: | E. Hrushovski M. Itai |
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| Affiliation: | Department of Mathematics, Hebrew University, Jerusalem, Israel ; Department of Mathematical Sciences, Tokai University, Hiratsuka 259-1292, Japan |
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| 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  . We show that this sub-family is usually definable (in particular if  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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