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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Diophantine sets over $ {\bf Z}[T]$


Author: J. Denef
Journal: Proc. Amer. Math. Soc. 69 (1978), 148-150
MSC: Primary 02F50; Secondary 10B99, 10N99
MathSciNet review: 0462934
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Abstract: Let $ {\mathbf{Z}}[T]$ be the ring of polynomials with integer coefficients. We prove that every recursively enumerable subset of $ {\mathbf{Z}}[T]$ is diophantine over $ {\mathbf{Z}}[T]$. This extends a theorem of Davis and Putnam which states that every recursively enumerable subset of Z is diophantine over $ {\mathbf{Z}}[T]$.


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DOI: https://doi.org/10.1090/S0002-9939-1978-0462934-X
Keywords: Diophantine sets, Hilbert's tenth problem, unsolvable problems, recursively enumerable sets, diophantine equations
Article copyright: © Copyright 1978 American Mathematical Society