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March 2010 Real closed fields and models of Peano arithmetic
P. D'Aquino, J. F. Knight, S. Starchenko
J. Symbolic Logic 75(1): 1-11 (March 2010). DOI: 10.2178/jsl/1264433906

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.

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P. D'Aquino. J. F. Knight. S. Starchenko. "Real closed fields and models of Peano arithmetic." J. Symbolic Logic 75 (1) 1 - 11, March 2010. https://doi.org/10.2178/jsl/1264433906

Information

Published: March 2010
First available in Project Euclid: 25 January 2010

zbMATH: 1186.03061
MathSciNet: MR2605879
Digital Object Identifier: 10.2178/jsl/1264433906

Rights: Copyright © 2010 Association for Symbolic Logic

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Vol.75 • No. 1 • March 2010
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