Undecidable extensions of Skolem arithmetic

DOI10.2307/2586837zbMath0911.03030OpenAlexW2099198433MaRDI QIDQ4212909

Alexis Bès, Denis Richard

Publication date: 7 October 1998

Published in: The Journal of Symbolic Logic (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2586837

zbMATH Keywords

coprimeness predicateundecidable extensions of Skolem arithmetic

Mathematics Subject Classification ID

First-order arithmetic and fragments (03F30)

Related Items (4)

Some new results in monadic second-order arithmetic ⋮ A note on definability in fragments of arithmetic with free unary predicates ⋮ A list of arithmetical structures complete with respect to the first-order definability ⋮ 2004 Summer Meeting of the Association for Symbolic Logic

Cites Work

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• All arithmetical sets of powers of primes are first-order definable in terms of the successor function and the coprimeness predicate
• The theory of integer multiplication with order restricted to primes is decidable
• Definability and decidability issues in extensions of the integers with the divisibility predicate
• Definability and decision problems in arithmetic

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