4 papers
Existentially closed fields with operators in various categories
Jakub Gogolok
We deal with fields with certain operators - introduced by the author and Kowalski - which we call -fields. We are mostly interested in -fields which are…
A note on valued fields with finite group actions
Piotr Błaszkiewicz, Jakub Gogolok
We consider valued fields equipped with an action of a given finite group by automorphisms. We show that the theory of such structures admits a model companion which is axiomatized…
Model theory of derivations of the Frobenius map revisited
Jakub Gogolok
We prove some results about the model theory of fields with a derivation of the Frobenius map, especially that the model companion of this theory is axiomatizable by axioms used by…
Operators coming from ring schemes
Jakub Gogolok, Piotr Kowalski
We introduce the notion of a coordinate -algebra scheme and the corresponding notion of a -operator. This class of operators includes endomorphisms and der…