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A recursive nonstandard model of normal open induction
Journal of Symbolic Logic 61 (4):1228-1241 (1996)
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 elementsAuthor's Profile
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Citations of this work
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Independence results for variants of sharply bounded induction.Leszek Aleksander Kołodziejczyk - 2011 - Annals of Pure and Applied Logic 162 (12):981-990.
Toward the Limits of the Tennenbaum Phenomenon.Paola D'Aquino - 1997 - Notre Dame Journal of Formal Logic 38 (1):81-92.
A Note on Recursive Models of Set Theories.Domenico Zambella & Antonella Mancini - 2001 - Notre Dame Journal of Formal Logic 42 (2):109-115.
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References found in this work
Primes and their residue rings in models of open induction.Angus Macintyre & David Marker - 1989 - Annals of Pure and Applied Logic 43 (1):57-77.
The joint embedding property in normal open induction.Margarita Otero - 1993 - Annals of Pure and Applied Logic 60 (3):275-290.
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