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Preprint Number 591
591. Jamshid Derakhshan and Angus Macintyre
Some supplements to Feferman-Vaught related to the model theory of adeles
Submission date: 7 June 2013.
We give foundational results for the model theory of the ring of finite adeles over a number field construed as a restricted product of local fields. In contrast to Weispfenning we work in the language of ring theory, and various sortings interpretable therein. In particular we give a systematic treatment of the product valuation and the valuation monoid. Deeper results are given for the adelic version of Krasner's hyperfields, relating them to the Basarab-Kuhlmann formalism.
Mathematics Subject Classification: Primary 03C10,03C40,03C60,03C95,03C98; Sec- ondary 11U05,11U09,12L05,12L12,12E50.
Keywords and phrases: Definability, Restricted Products and Adeles, Quantifier Elimination, Feferman-Vaught Theorems, Hyperrings, Valued Fields.
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