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Diophantine sets of polynomials over number fields

Author(s): Jeroen Demeyer
Journal: Proc. Amer. Math. Soc. 138 (2010), 2715-2728.
MSC (2010): Primary 11U09; Secondary 03D25, 11D99, 11R09, 12E10
Posted: April 5, 2010
MathSciNet review: 2644887
Retrieve article in: PDF

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Abstract: Let $\mathcal{R}$ be a number field or a recursive subring of a number field and consider the polynomial ring $\mathcal{R}[T]$ . We show that the set of polynomials with integer coefficients is diophantine over $\mathcal{R}[T]$ . Applying a result by Denef, this implies that every recursively enumerable subset of $\mathcal{R}[T]^k$ is diophantine over $\mathcal{R}[T]$ .

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