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Modèle complétude des structures o-minimales polynomialement bornées

Abstract : 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.
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Contributor : Olivier Le Gal <>
Submitted on : Monday, January 29, 2007 - 6:30:53 PM
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  • HAL Id : tel-00127811, version 1


Olivier Le Gal. Modèle complétude des structures o-minimales polynomialement bornées. Mathématiques [math]. Université Rennes 1, 2006. Français. ⟨tel-00127811⟩



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