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Transactions of the American Mathematical Society

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On model complete differential fields

Authors: E. Hrushovski and M. Itai
Journal: Trans. Amer. Math. Soc. 355 (2003), 4267-4296
MSC (2000): Primary 03C60, 12H05
Published electronically: July 8, 2003
MathSciNet review: 1990753
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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 $X$. 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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Additional Information

E. Hrushovski
Affiliation: Department of Mathematics, Hebrew University, Jerusalem, Israel

M. Itai
Affiliation: Department of Mathematical Sciences, Tokai University, Hiratsuka 259-1292, Japan

Received by editor(s): August 1, 1998
Published electronically: July 8, 2003
Additional Notes: The first author thanks Miller Institute at the University of California, Berkeley
Article copyright: © Copyright 2003 American Mathematical Society