We prove that for a finite collection of sets definable in an o-minimal structure there exists a compatible definable stratification such that for any stratum the fibers of its projection onto satisfy the Whitney property with exponent 1.
We present the history of the development of Picard-Vessiot theory for linear ordinary differential equations. We are especially concerned with the condition of not adding new constants, pointed out by R. Baer. We comment on Kolchin's condition of algebraic closedness of the subfield of constants of the given differential field over which the equation is defined. Some new results concerning existence of a Picard-Vessiot extension for a homogeneous linear ordinary differential equation defined over...
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