A recursive nonstandard model of normal open induction-Reference-Cited by-同舟云学术

A recursive nonstandard model of normal open induction

Published:1996-12 Issue:4 Volume:61 Page:1228-1241
ISSN:0022-4812
Container-title:Journal of Symbolic Logic
language:en
Short-container-title:J. symb. log.

Author:

Berarducci Alessandro,Otero Margarita

Abstract

AbstractModels 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.

Publisher

Cambridge University Press (CUP)

Subject

Logic,Philosophy

Reference17 articles.

1. Some model theory and number theory for models of weak systems of arithmetic

2. A nonstandard model for a free variable fragment of number theory;Shepherdson;Bulletin of the Polish Academy of Sciences,1964

Cited by 7 articles. 订阅此论文施引文献订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献

1. Real closures of models of weak arithmetic;Archive for Mathematical Logic;2012-11-13

2. Independence results for variants of sharply bounded induction;Annals of Pure and Applied Logic;2011-12

3. Limit computable integer parts;Archive for Mathematical Logic;2011-06-18

4. 2008 European Summer Meeting of the Association for Symbolic Logic. Logic Colloquium '08;The Bulletin of Symbolic Logic;2009-03

5. A Note on Recursive Models of Set Theories;Notre Dame Journal of Formal Logic;2001-04-01