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On model complete differential fields
Author(s):
E.
Hrushovski;
M.
Itai
Journal:
Trans. Amer. Math. Soc.
355
(2003),
4267-4296.
MSC (2000):
Primary 03C60, 12H05
Posted:
July 8, 2003
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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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Additional Information:
E.
Hrushovski
Affiliation:
Department of Mathematics, Hebrew University, Jerusalem, Israel
Email:
ehud@sunset.ma.huji.ac.il
M.
Itai
Affiliation:
Department of Mathematical Sciences, Tokai University, Hiratsuka 259-1292, Japan
Email:
itai@ss.u-tokai.ac.jp
DOI:
10.1090/S0002-9947-03-03264-1
PII:
S 0002-9947(03)03264-1
Received by editor(s):
August 1, 1998
Posted:
July 8, 2003
Additional Notes:
The first author thanks Miller Institute at the University of California, Berkeley
Copyright of article:
Copyright
2003,
American Mathematical Society
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