The theory of modules of separably closed fields. I

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Journal of Symbolic Logic 67 (3):997-1015 (2002)
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Abstract

We consider separably closed fields of characteristic $p > 0$ and fixed imperfection degree as modules over a skew polynomial ring. We axiomatize the corresponding theory and we show that it is complete and that it admits quantifier elimination in the usual module language augmented with additive functions which are the analog of the $p$-component functions.

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Citations of this work

Subgroups of the additive group of a separably closed field.Thomas Blossier - 2005 - Annals of Pure and Applied Logic 134 (2-3):169-216.
The theory of modules of separably closed fields 2.Pilar Dellunde, Françoise Delon & Françoise Point - 2004 - Annals of Pure and Applied Logic 129 (1-3):181-210.

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References found in this work

Model theory.Wilfrid Hodges - 2008 - Stanford Encyclopedia of Philosophy.
Model theory of modules.Martin Ziegler - 1984 - Annals of Pure and Applied Logic 26 (2):149-213.
Notes on the stability of separably closed fields.Carol Wood - 1979 - Journal of Symbolic Logic 44 (3):412-416.
Minimal types in separably closed fields.Zoé Chatzidakis & Carol Wood - 2000 - Journal of Symbolic Logic 65 (3):1443-1450.
Forking in modules.Steven Garavaglia - 1981 - Notre Dame Journal of Formal Logic 22 (2):155-162.

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