Submission date: 5 November 2007

Abstract:

We prove that the zero-set of a C-infinity function belonging to a noetherian differential ring M can be written as a finite union of C-infinity manifolds which are definable by functions from the same ring. These results hold not only over the reals, but more generally for definable C-infinity functions in a definably complete expansion of an ordered field. We provide examples of noetherian differential rings of C-infinity functions over the reals, containing non-analytic functions.

Mathematics Subject Classification: 03C64, 26E10 and 26E30

Keywords and phrases: Noetherian Varieties, Definable completeness, o-minimality, Quasi-analytic functions

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