Submission date: 31 March 2016.

Abstract:

We study the model theory of the ring of adeles of a number field. We obtain quantifier elimination results in the language of rings and some enrichments. We given consequences for definable subsets of the adeles, and their measures.

Mathematics Subject Classification: 03C10, 11M06, 11M41, 11U09, 11U05, 11U07, 11S40, 12J12, 12J25, 12J10

Keywords and phrases:

Full text arXiv 1603.09698: pdf, ps.