On the value group of a model of Peano Arithmetic

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.