2013/06/07 by Jamshid Derakhshan, Angus Macintyre, Derakhshan, Jamshid +1
Mathematics · #03C40 #03C60 #03C95 #03C98 #11U09 #12E50 #12L05 #12L12 #FOS: Mathematics #Logic (math.LO) #Primary 03C10 #Secondary 11U05 #math.LO #msc:03C10 #msc:03C40 #msc:03C60 #msc:03C95 #msc:03C98 #msc:11U05 #msc:11U09 #msc:12E50 #msc:12L05 #msc:12L12
paper · pdf · doi:10.48550/arxiv.1306.1794
arxiv created 2013/06/07 · arxiv updated 2013/06/10
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.