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Elementary properties of power series fields over finite fields

Franz-Viktor Kuhlmann
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Abstract

In spite of the analogies between Q_p and F_p((t)) which became evident through the work of Ax and Kochen, an adaptation of the complete recursive axiom system given by them for Q_p to the case of F_p((t)) does not render a complete axiom system. We show the independence of elementary properties which express the action of additive polynomials as maps on F_p((t)). We formulate an elementary property expressing this action and show that it holds for all maximal valued fields. We also discuss the action of arbitrary polynomials on valued fields.

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Franz-Viktor Kuhlmann. 1998-07-01. Elementary properties of power series fields over finite fields. https://arxiv.org/abs/math/9807186

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