The elementary theory of large fields of totally S-adic numbers
Arno Fehm
TL;DR
This paper studies the logical properties of fields composed of totally S-adic algebraic numbers, providing axioms and proving their theories are decidable, thus generalizing previous classical results.
Contribution
It offers a new axiomatization and proves decidability for the elementary theories of these fields, extending prior classical results.
Findings
Axiomatization of the theories of totally S-adic fields
Decidability of these theories established
Generalization of classical decidability results
Abstract
We analyze the elementary theory of certain fields of totally S-adic algebraic numbers that were introduced and studied by Geyer-Jarden and Haran-Jarden-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-Kiehne, Fried-Haran-V\"olklein and Ershov.
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