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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

LEONIDAS CERDA-ROMERO  and
CARLOS MARTINEZ-RANERO
LEONIDAS CERDA-ROMERO
Affiliation:
DEPARTAMENTO DE MATEMÁTICA UNIVERSIDAD DE CONCEPCIÓN CASILLA 160-C, CONCEPCIÓN CHILE E-mail: leonidascerda@udec.cl ESCUELA SUPERIOR POLITÉCNICA DE CHIMBORAZO RIOBAMBA, ECUADOR E-mail: lcerda@espoch.edu.ec
CARLOS MARTINEZ-RANERO
Affiliation:
DEPARTAMENTO DE MATEMÁTICA UNIVERSIDAD DE CONCEPCIÓN CASILLA 160-C, CONCEPCIÓN CHILE E-mail: cmartinezr@udec.cl
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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.

Keywords

11U05positive-existential definabilityS-integerssmall rings

Information

Type
Articles
Information
The Journal of Symbolic Logic , Volume 82 , Issue 3 , September 2017 , pp. 1140 - 1149
Copyright
Copyright © The Association for Symbolic Logic 2017 

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