Model theory of fields with free operators in positive characteristic

Beyarslan, Özlem; Hoffmann, Daniel Max; Kamensky, Moshe; Kowalski, Piotr

doi:10.1090/tran/7896

Model theory of fields with free operators in positive characteristic
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by Özlem Beyarslan, Daniel Max Hoffmann, Moshe Kamensky and Piotr Kowalski PDF

Trans. Amer. Math. Soc. 372 (2019), 5991-6016 Request permission

Abstract:

We give algebraic conditions for a finite commutative algebra $B$ over a field of positive characteristic, which are equivalent to the companionability of the theory of fields with “$B$-operators” (i.e., the operators coming from homomorphisms into tensor products with $B$). We show that, in the most interesting case of a local $B$, these model companions admit quantifier elimination in the “smallest possible” language, and they are strictly stable. We also describe the forking relation there.

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