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THE DIOPHANTINE PROBLEM FOR ADDITION AND DIVISIBILITY OVER SUBRINGS OF THE RATIONALS
Published online by Cambridge University Press: 08 September 2017
Abstract
It is shown that the positive existential theory of the structure (ℤ[S−1]; =, 0, 1, + , |), 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 (ℤ; =, 0, 1, + |) is decidable.
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- Copyright © The Association for Symbolic Logic 2017
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