Diophantine Sets of Polynomials over Number Fields
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Thu, 28/01/2010 17:00 |
Jeroen Demeyer (Ghent) |
Logic Seminar  |
L3 |
| Let R be a number field (or a recursive subring of anumber field) and consider the polynomial ring R[T].We show that the set of polynomials with integercoefficients is diophantine (existentially definable) over R[T].Applying a result by Denef, this implies that everyrecursively enumerable subset of R[T]^k is diophantine over R[T]. | |||