Model Theory of Adeles I

2016/03/31 by Derakhshan, Jamshid, Macintyre, Angus
#03C10 #11M06 #11M41 #11S40 #11U05 #11U07 #11U09 #12J10 #12J12 #12J25 #FOS: Mathematics #Logic (math.LO)

paper · doi:10.48550/arxiv.1603.09698

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.

Related

• Model Theory of Adeles and Number Theory
• Some supplements to Feferman-Vaught related to the model theory of adeles
• Formalizing the Ring of Adèles of a Global Field
• Decidability Problems for Adele Rings and related restricted products
• Formalising the local compactness of the adele ring