On Diophantine Definability and Decidability in Some Infinite Totally Real Extensions of Q
نویسنده
چکیده
Let M be a number field, and WM a set of its non-Archimedean primes. Then let OM,WM = {x ∈M | ordt x ≥ 0, ∀t 6∈ WM}. Let {p1, . . . , pr} be a finite set of prime numbers. Let Finf be the field generated by all the pji -th roots of unity as j → ∞ and i = 1, . . . , r. Let Kinf be the largest totally real subfield of Finf . Then for any ε > 0, there exist a number field M ⊂ Kinf , and a set WM of non-Archimedean primes of M such that WM has density greater than 1 − ε, and Z has a Diophantine definition over the integral closure of OM,WM in Kinf .
منابع مشابه
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