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Proceedings of the American Mathematical Society

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

 

 

Decidability of the existential theory of the set of natural numbers with order, divisibility, power functions, power predicates, and constants


Author: Véronique Terrier
Journal: Proc. Amer. Math. Soc. 114 (1992), 809-816
MSC: Primary 03B25; Secondary 03F30
MathSciNet review: 1072092
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Abstract: We construct an algorithm to test if a system of conditions of the types $ \mu < \eta ,\mu /\eta ,\mu = {\eta ^a},{P_a}(\mu ),\neg (\mu < \eta ),\neg (\mu /\eta ),\neg (\mu = {\eta ^a})$, and $ \neg ({P_a}(\mu ))$ has a solution in natural numbers. ($ a \in N$, and $ {P_a}$ denotes the set $ \{ {n^a}:n \in N\} $.)


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DOI: https://doi.org/10.1090/S0002-9939-1992-1072092-6
Keywords: Decision problems in arithmetic, decidability
Article copyright: © Copyright 1992 American Mathematical Society