Algebraically Closed Fields with a Generic Multiplicative Character

2017/04/30 by Hakobyan, Tigran, Tran, Minh Chieu
#03B25 #03C10 #03C65 #12L12 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1705.00261

Abstract

We study the model theory of the 2-sorted structure (\mathbbF, ℂ;χ), where \mathbbF is an algebraic closure of a finite field of characteristic p, ℂ is the field of complex numbers and χ: \mathbbF → ℂ is an injective, multiplication preserving map. We obtain an axiomatization ACFC_p of Th(\mathbbF,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.

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