Submission date: 19 August 2014

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-Völklein and Ershov.

Mathematics Subject Classification: 12E30, 12F10, 20E18, 03C60

Keywords and phrases:

Full text arXiv 1408.4234: pdf, ps.