English

Generic multiplicative endomorphism of a field

Logic 2025-01-20 v4

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 NSOP1_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.

Keywords

Cite

@article{arxiv.2212.02115,
  title  = {Generic multiplicative endomorphism of a field},
  author = {Christian d'Elbée},
  journal= {arXiv preprint arXiv:2212.02115},
  year   = {2025}
}

Comments

36 pages

R2 v1 2026-06-28T07:22:00.867Z