Elimination des quantificateurs dans le cadre quasi-analytique

Abstract : We associate to every compact polydisk B [belonging to ] Rn an algebra CB of real functions defined in a neighborhood of B. The collection of these algebras is supposed to be closed under several operations, such as composition and partial derivatives. Moreover, if the center of B is the origin, we assume that the algebra of germs at the origin of elements of CB is quasianalytic (it does not contain any flat germ). We define with these functions the collection of C-semianalytic and C-subanalytic sets according to the classical process in real analytic geometry. Our main result is an analogue of Tarski-Seidenberg's usual result for these sets. It says that the sub-C-subanalytic sets may be described by means of equalities and inequalities by terms obtained by composition of elements of the algebras CB, the functions x->^{1/n} and the function x->1/x. It is proved via a model theoretic preparation theorem
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Francois Michas. Elimination des quantificateurs dans le cadre quasi-analytique. Mathématiques générales [math.GM]. Université de Bourgogne, 2012. Français. ⟨NNT : 2012DIJOS013⟩. ⟨tel-00783864⟩

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