Generic multiplicative endomorphism of a field

2022/12/05 by Christian d’Elbée, d'Elbée, Christian · 1 citation
Computer Science · #03C10 #03C45 #03C60 #Distributed and Parallel Computing Systems #FOS: Mathematics #Logic (math.LO)

paper · pdf · doi:10.48550/arxiv.2212.02115

openalex publication_date 2022/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

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 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.

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• Generic derivations on algebraically bounded structures II Model theoretical properties

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