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Sur les collapses de corps différentiels colorés en caractéristique nulle décrits par Poizat à l'aide des amalgames à la Hrushovski

Part of: Model theory

Published online by Cambridge University Press:  16 October 2008

T. Blossier  and
A. Martin-Pizarro
T. Blossier
Affiliation:
Université de Lyon, Université Lyon 1, INSA de Lyon, F-69621, Ecole Centrale de Lyon, CNRS, UMR5208, Institut Camille Jordan, 43 boulevard du 11 novembre 1918, F-69622 Villeurbanne-Cedex, France, (blossier@math.univ-lyon1.fr).
A. Martin-Pizarro
Affiliation:
Institut für Mathematik, Humboldt-Universität zu Berlin, D–10099 Berlin, Allemagne, (pizarro@mathematik.hu-berlin.de).
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Abstract

We apply the collapse techniques to Poizat's red differential field in order to obtain differentially closed fields of Morley rank ω·2 each equipped with an additive definable subgroup of rank ω. By means of the logarithmic derivative, we obtain a green field of rank ω·2 with a multiplicative definable divisible subgroup containing the field of constants, which is again definable in the reduct of the green field.

Résumé

Nous collapsons le corps différentiel rouge de Poizat en des corps différentiellement clos de rang de Morley ω·2, chacun muni d'un sous-groupe additif définissable de rang ω. En utilisant la dérivée logarithmique, on obtient un corps vert de rang ω·2 avec un sous-groupe multiplicatif définissable divisible contenant le corps des constantes, qui reste définissable dans le réduit à la structure de corps vert.

Keywords

théorie des modèlescorps différentiellement closamalgamesmodel theorydifferentially closed fieldsamalgamation method

MSC classification

Secondary: 03C65: Models of other mathematical theories 03C50: Models with special properties (saturated, rigid, etc.)
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 8 , Issue 3 , July 2009 , pp. 445 - 464
Copyright
Copyright © Cambridge University Press 2008

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