Submission date: 23 January 2014.

Abstract:

We deal with two foundational questions on complete differential algebraic varieties. We establish, by means of the differential algebraic version of Bertini's theorem and assuming a weaker form of the catenary conjecture, that in order to verify (differential) completeness one can restrict second factors to zero-dimensional differential varieties. Then, we extend Kolchin's results on linear dependence over projective varieties in the constants, to linear dependence over arbitrary complete differential varieties.

Mathematics Subject Classification: 03C60, 12H05

Keywords and phrases: differential algebraic geometry, model theory

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