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Zbl 0873.32004
Lion, Jean-Marie; Rolin, Jean-Philippe
Théorème de préparation pour les fonctions logarithmico-exponentielles. (Preparation theorem for logarithmico-exponential functions). (French)
[J] Ann. Inst. Fourier 47, No.3, 859-884 (1997). ISSN 0373-0956; ISSN 1777-5310/e

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

MSC 2000:: *32B05 Analytic algebras and generalizations
32B20 Semi-analytic sets, etc.
14P15 Real analytic and semianalytic sets

Keywords: semi-analytic sets; sub-analytic sets; exponential; logarithm; quantifier elimination; preparation theorem

Cited in: Zbl 1216.26008 Zbl 1181.14062 Zbl 1034.32007 Zbl 1081.03039 Zbl 1027.32013 Zbl 0912.32007

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