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.
Real closed fields and models of Peano Arithmetic
D'AQUINO, Paola;
2010
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.File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
