# Some supplements to Feferman-Vaught related to the model theory of adeles

Derakhshan, J
Macintyre, A

## Journal:

Annals of Pure and Applied Logic

## Last Updated:

2019-09-01T00:32:09.993+01:00

11

165

## abstract:

We give foundational results for the model theory of $\Bbb A_K^{fin}$, 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.

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