6533b873fe1ef96bd12d53bc
RESEARCH PRODUCT
Quantifier elimination in the quasi-analytic framework
Francois Michassubject
[MATH.MATH-GM]Mathematics [math]/General Mathematics [math.GM]Tarsk-Seidenberg theoremThéorème de Tarski-SeidenbergAlgèbres quasianalytiques[ MATH.MATH-GM ] Mathematics [math]/General Mathematics [math.GM]Real analytic geometryQuasianalytic algebrasThéorème de préparationStructures o-minimales[MATH.MATH-GM] Mathematics [math]/General Mathematics [math.GM]O-minimal structuresPreparation theoremGéométrie analytique réelledescription
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
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2012-06-21 |