Journal of Symbolic Logic

A Recursive Nonstandard Model of Normal Open Induction

Alessandro Berarducci and Margarita Otero

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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.

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J. Symbolic Logic, Volume 61, Issue 4 (1996), 1228-1241.

First available in Project Euclid: 6 July 2007

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Berarducci, Alessandro; Otero, Margarita. A Recursive Nonstandard Model of Normal Open Induction. J. Symbolic Logic 61 (1996), no. 4, 1228--1241.

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