Quasi-analycité, o-minimalité et élimination des quantificateurs

Autor: Rambaud, Alexandre
Přispěvatelé: Équipe de Logique Mathématique (ELM), Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Allocation de recherche de l'Université Paris 7 et Monitorat à l'Université Paris 12, Univeristé Paris Diderot Paris 7, Jean-Pierre Ressayre
Jazyk: francouzština
Rok vydání: 2005
Předmět:
Zdroj: Logique [math.LO]. Univeristé Paris Diderot Paris 7, 2005. Français
Popis: This thesis studies from the point of view of model theory and topology certain classes of real functions : restricted quasi-analytic functions. Here, a restricted quasi-analytic class E will consist on the one hand of a ring of real functions C ∞, which vanish outside a compact box, containing the indicator functions of every compact box and which is closed by composition, rational powers, implicit functions and C ∞ division. On the other hand, we will require every C ∞ function around 0 either to vanish around 0 or to have a finite multiplicity. For such a given class E, we consider the language L which contains the langage of rings, a symbol for each function of E and one more for the order ; we study the universal theory T in the language L such that T contains the theory of ordered rings and the universal axioms which define the indicator functions of compact boxes, rational powers, implicit functions, C ∞ division, the simple diagram of R (real numbers) and the boundedness of the functions of E on a compact box. We prove that T is equivalent to the complete theory of R in the language L and is model-complete. In particular, T admits quantifiers elimination because T is universal. Furthermore, T is o-minimal and admits local cellular decompositions in terms of E.; Cette thèse étudie selon le point de vue de la théorie des modèles certaines classes de fonctions réelles : les classes quasi-analytiques restreintes. Soit E une telle classe, on explicite un langage naturel L contenant E et une théorie T dans L tels que T admet l’élimination des quantificateurs, est o-minimale et est équivalente à la théorie complète de R dans L.
Databáze: OpenAIRE