Submission date: 5 December 2022

Abstract:

We introduce the model-companion of the theory of fields expanded by a unary function for a multiplicative map, which we call ACFH. Among others, we prove that this theory is NSOP_1 and not simple, that the kernel of the map is a generic pseudo-finite abelian group. We also prove that if forking satisfies existence, then ACFH has elimination of imaginaries.

Mathematics Subject Classification: 03C45, 03C10, 03C60

Keywords and phrases:

Full text arXiv 2212.02115: pdf, ps.