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

Abstract

AbstractNon-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 Kolehin in the context of differentially closed fields. It yields some orthogonality and stratification results.