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On the Relationship Between Matiyasevich's and Smorynski's Theorems

2019
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Scientific Annals of Computer Science
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Yuri Matiyasevich's theorem states that the set of all Diophantine equations which have a solution in non-negative integers is not recursive. Craig Smoryński's theorem states that the set of all Diophantine equations which have at most finitely many solutions in non-negative integers is not recursively enumerable. Let R be a subring of Q with or without 1. By H_10(R), we denote the problem of whether there exists an algorithm which for any given Diophantine equation with integer coefficients,

doi:10.7561/sacs.2019.1.101
fatcat:55pyonfn5jatvlxee5hqrf3jse