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

Author: 

Derakhshan, J
Macintyre, A

Journal: 

Annals of Pure and Applied Logic

Last Updated: 

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

Issue: 

11

Volume: 

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.

Symplectic id: 

737395

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article