Real closed fields and models of Peano arithmetic

Journal of Symbolic Logic 75 (1):1-11 (2010)
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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

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References found in this work

Recursively saturated models generated by indiscernibles.James H. Schmerl - 1985 - Notre Dame Journal of Formal Logic 26 (2):99-105.

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