Generic multiplicative endomorphism of a field

Generic multiplicative endomorphism of a field

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 s...

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1. Verfasser: d'Elbée, Christian
Format: Artikel
Sprache:eng
Schlagworte:
Mathematics - Logic
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Zusammenfassung: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.
DOI:10.48550/arxiv.2212.02115