Journal of Symbolic Logic

Une fonction de Kolchin pour les corps imparfaits de degré d'imperfection fini

Françoise Delon

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Non-perfect separably closed fields are stable, and not superstable. As a result, not all types can be ranked. We develop here a new tool, a “semi-rank”, which takes values in the non-negative reals, and gives a sufficient condition for forking of types. This semi-rank is built up from a transcendence function, analogous to the one considered by Kolchin in the context of differentially closed fields. It yields some orthogonality and stratification results.


Un corps séparablement clos non algébriquement clos est stable sans être superstable. Cela signifie que seuls certains de ses types sont rangés. Nous développons un autre outil, un « semi-rang » à valeurs réelles, qui donne un critère de déviation des types. Ce semi-rang est construit à partir d'un analogue de la fonction de Kolchin associée à un type au-dessus d'un corps différentiel. Il produit des résultats de stratification des modèles et des résultats d'orthogonalité.

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J. Symbolic Logic, Volume 70, Issue 2 (2005), 664-680.

First available in Project Euclid: 1 July 2005

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Delon, Françoise. Une fonction de Kolchin pour les corps imparfaits de degré d'imperfection fini. J. Symbolic Logic 70 (2005), no. 2, 664--680. doi:10.2178/jsl/1120224735.

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