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THE ELEMENTARY THEORY OF LARGE FIELDS OF TOTALLY $\mathfrak{S}$-ADIC NUMBERS

Published online by Cambridge University Press:  23 April 2015

Arno Fehm
Arno Fehm*
Affiliation:
University of Konstanz, Department of Mathematics and Statistics, 78457 Konstanz, Germany (arno.fehm@uni-konstanz.de)
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Abstract

We analyze the elementary theory of certain fields $K^{\mathfrak{S}}(\boldsymbol{\unicode[STIX]{x1D70E}})$ of totally $\mathfrak{S}$-adic algebraic numbers that were introduced and studied by Geyer and Jarden and by Haran, Jarden, and Pop. In particular, we provide an axiomatization of these theories and prove their decidability, thereby giving a common generalization of classical decidability results of Jarden and Kiehne, Fried, Haran, and Völklein, and Ershov.

Keywords

totally S-adic numbersabsolute Galois groupmodel theory of profinite groupsdecidability of fields
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 16 , Issue 1 , February 2017 , pp. 121 - 154
Copyright
© Cambridge University Press 2015 

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