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Preprint Number 1215

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1215. Tigran Hakobyan, Minh Chieu Tran
Algebraically Closed Fields with a Generic Multiplicative Character

Submission date: 30 April 2017


We study the model theory of the 2-sorted structure (F, C;χ), where F is an algebraic closure of a finite field of characteristic p, C is the field of complex numbers and χ: F → C is an injective, multiplication preserving map. We obtain an axiomatization ACFC_p of Th(F,C;χ) in a suitable language L, classify the models of ACFC_p up to isomorphism, prove a modified model companion result, give various descriptions of definable sets inside a model of ACFC_p, and deduce that ACFC_p is ω-stable and has definability of Morley rank in families.

Mathematics Subject Classification: 03C65, 03B25, 03C10, 12L12

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Full text arXiv 1705.00261: pdf, ps.

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