We investigate IPA-real closed fields, that is, real closed fields which admit an integer part whose non-negative cone is a model of Peano arithmetic. We show that the value group of an IPA-real closed field is an exponential group in the residue field, and that the converse fails in general. As an application, we classify (up to isomorphism) value groups of countable recursively saturated exponential real closed fields. We exploit this characterization to construct countable exponential real closed fields which are not IPA-real closed fields.

On the value group of a model of Peano Arithmetic

D'AQUINO, Paola;
2017

Abstract

We investigate IPA-real closed fields, that is, real closed fields which admit an integer part whose non-negative cone is a model of Peano arithmetic. We show that the value group of an IPA-real closed field is an exponential group in the residue field, and that the converse fails in general. As an application, we classify (up to isomorphism) value groups of countable recursively saturated exponential real closed fields. We exploit this characterization to construct countable exponential real closed fields which are not IPA-real closed fields.
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.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11591/368320
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 6
  • ???jsp.display-item.citation.isi??? 3
social impact