caa a22 4500 388039191 CHVBK 20180307125016.0 cr unu---uuuuu 161130e199806 xx s 000 0 eng 10.2307/2586837 doi S002248120001495X pii (NATIONALLICENCE)cambridge-10.2307/2586837 Undecidable extensions of Skolem arithmetic [Elektronische Daten] Let be the restriction of usual order relation to integers which are primes or squares of primes, and let ⊥ denote the coprimeness predicate. The elementary theory of is undecidable. Now denote by <π the restriction of order to primary numbers. All arithmetical relations restricted to primary numbers are definable in the structure (ℕ; ⊥, <π). Furthermore, the structures (ℕ; ∣, <π) (ℕ; =, ×, <π) and (ℕ; =, +, ×) are interdefinable. Copyright © Association for Symbolic Logic 1998 Bès Alexis Equipe de Logique, Université Paris 7, 2, Place Jussieu, 75251 Paris Cedex 05, France, E-mail: bes@logique.jussieu.fr Richard Denis Laboratoire de Logique, Algorithmique, et Informatique de Clermont I (LLAIC 1), I. U. T. Informatique, B. P. 86, F-63172 Aubière Cedex, France, E-mail: richard@llaic.u-clermontl.fr The Journal of Symbolic Logic Cambridge University Press 63/2(1998-06), 379-401 0022-4812 63:2<379 1998 63 JSL https://doi.org/10.2307/2586837 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.2307/2586837 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bès Alexis Equipe de Logique, Université Paris 7, 2, Place Jussieu, 75251 Paris Cedex 05, France, E-mail: bes@logique.jussieu.fr NATIONALLICENCE 700 1- Richard Denis Laboratoire de Logique, Algorithmique, et Informatique de Clermont I (LLAIC 1), I. U. T. Informatique, B. P. 86, F-63172 Aubière Cedex, France, E-mail: richard@llaic.u-clermontl.fr NATIONALLICENCE 773 0- The Journal of Symbolic Logic Cambridge University Press 63/2(1998-06), 379-401 0022-4812 63:2<379 1998 63 JSL CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-cambridge