Generic multiplicative endomorphism of a field
arXiv:2212.02115
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 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.
36 pages