Théorème de préparation pour les fonctions logarithmico-exponentielles
Annales de l'Institut Fourier, Volume 47 (1997) no. 3, p. 859-884

We give a geometric proof of the quantifier elimination theorem for logarithmico-exponential functions, already proved by van den Dries, Macintyre and Marker. Our proof does not make use of model theory arguments. It is based upon a preparation theorem for subanalytic functions.

Nous donnons une preuve géométrique du théorème d’élimination des quantificateurs pour les fonctions logarithmico-exponentielles prouvé initialement par van den Dries, Macintyre et Marker. Notre démonstration n’utilise pas de Théorie des Modèles. Elle repose sur un théorème de préparation pour les fonctions sous-analytiques.

@article{AIF_1997__47_3_859_0,
     author = {Lion, Jean-Marie and Rolin, Jean-Philippe},
     title = {Th\'eor\`eme de pr\'eparation pour les fonctions logarithmico-exponentielles},
     journal = {Annales de l'Institut Fourier},
     publisher = {Association des Annales de l'institut Fourier},
     volume = {47},
     number = {3},
     year = {1997},
     pages = {859-884},
     doi = {10.5802/aif.1583},
     zbl = {0873.32004},
     mrnumber = {98h:32009},
     language = {fr},
     url = {http://www.numdam.org/item/AIF_1997__47_3_859_0}
}
Lion, Jean-Marie; Rolin, Jean-Philippe. Théorème de préparation pour les fonctions logarithmico-exponentielles. Annales de l'Institut Fourier, Volume 47 (1997) no. 3, pp. 859-884. doi : 10.5802/aif.1583. http://www.numdam.org/item/AIF_1997__47_3_859_0/

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