The diophantine problem for addition and divisibility over subrings of the rationals

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Journal of Symbolic Logic 82 (3):1140-1149 (2017)
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Abstract

It is shown that the positive existential theory of the structure, where S is a nonempty finite set of prime numbers, is undecidable. This result should be put in contrast with the fact that the positive existential theory of is decidable.

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10.1017/jsl.2016.64

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Definability and decision problems in arithmetic.Julia Robinson - 1949 - Journal of Symbolic Logic 14 (2):98-114.
Defining integers.Alexandra Shlapentokh - 2011 - Bulletin of Symbolic Logic 17 (2):230-251.

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