Journal of Symbolic Logic

Real closed fields and models of Peano arithmetic

P. D'Aquino, J. F. Knight, and S. Starchenko

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Abstract

Shepherdson [14] showed that for a discrete ordered ring I, I is a model of IOpen iff I is an integer part of a real closed ordered field. In this paper, we consider integer parts satisfying PA. We show that if a real closed ordered field R has an integer part I that is a nonstandard model of PA (or even IΣ₄), then R must be recursively saturated. In particular, the real closure of I, RC(I), is recursively saturated. We also show that if R is a countable recursively saturated real closed ordered field, then there is an integer part I such that R = RC(I) and I is a nonstandard model of PA.

Article information

Source
J. Symbolic Logic, Volume 75, Issue 1 (2010), 1-11.

Dates
First available in Project Euclid: 25 January 2010

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1264433906

Digital Object Identifier
doi:10.2178/jsl/1264433906

Mathematical Reviews number (MathSciNet)
MR2605879

Zentralblatt MATH identifier
1186.03061

Citation

D'Aquino, P.; Knight, J. F.; Starchenko, S. Real closed fields and models of Peano arithmetic. J. Symbolic Logic 75 (2010), no. 1, 1--11. doi:10.2178/jsl/1264433906. https://projecteuclid.org/euclid.jsl/1264433906


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