Submission date: 12 April 2017

Abstract:

We study the model theory of (F;<_χ) where the field F is an algebraic closure of a finite field and <_χ is an ordering on the multiplicative group F^× induced by a group embedding χ: F^× \to F^×. Using number-theoretic bounds on multiplicative character sums over finite fields and Weyl's criterion for equidistribution, we establish a number of properties about the interaction between <_χ and the underlying field structure. We obtain a first-order axiomatization of these properties and show that the resulting theory is strongly model complete and has NTP_2.

Mathematics Subject Classification: Primary 03C65, Secondary 03B25, 03C10, 03C64, 11T24, 12L12

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Full text arXiv 1704.03853: pdf, ps.