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A recursive nonstandard model of normal open induction

Published online by Cambridge University Press:  12 March 2014

Alessandro Berarducci  and
Margarita Otero
Alessandro Berarducci
Affiliation:
Universitá di Pisa, Dipartamento Matematica, Via Buonarroti 2, 56127 Pisa, Italy, E-mail: [email protected]
Margarita Otero
Affiliation:
Universidad Autónoma de Madrid, Departamento Matemáticas, Ciudad Universidad de Canto Blanco, 28049 Madrid, Spain, E-mail: [email protected]
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Abstract

Models of normal open induction are those normal discretely ordered rings whose nonnegative part satisfy Peano's axioms for open formulas in the language of ordered semirings. (Where normal means integrally closed in its fraction field.)

In 1964 Shepherdson gave a recursive nonstandard model of open induction. His model is not normal and does not have any infinite prime elements.

In this paper we present a recursive nonstandard model of normal open induction with an unbounded set of infinite prime elements.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 61 , Issue 4 , December 1996 , pp. 1228 - 1241
Copyright
Copyright © Association for Symbolic Logic 1996

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References

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