Modèle complétude des structures o-minimales polynomialement bornées
Olivier Le Gal · HAL (Le Centre pour la Communication Scientifique Directe) · 2006
O-minimal structures were introduced in the 80' by Van den Dries answering the Grotendick's request for a tame geomety framework, and were largely studied by Wilkie and Macintyre. This thesis shows an explicit theorem of the complement for o-minimal polynomially bounded structures, result equivalent to the model-completness in model theorie. In 1968, Gabrielov shows a theorem of the complement for sub-analytic sets, which implice the tameness of global sub-analytics sets. He gives in 1996 an explicit version of this result. A generalisation of this theorem is introduced here. By valuation's arguments (due to Lojasiewicz in the analytic case and to Miller for the o-minimal case), some quasi-analytic's properties are exhibits, which permit to adapt the classical proof of model-completness sheme. This result is a step for better understand how o-minimal structures are generated and gives a reduced language on which an o-minimal polynomially bounded structure is model-complete.