Liouville closed HT-fields

Abstract

Let T be a complete, model complete o-minimal theory extending the theory of real closed ordered fields. An HT-field is a model K of T equipped with a T-derivation ▪ such that the underlying ordered differential field of ▪ is an H-field. We study HT-fields and their extensions. Our main result is that if T is power bounded, then every HT-field K has either exactly one or exactly two minimal Liouville closed HT-field extensions up to K-isomorphism. The assumption of power boundedness can be relaxed to allow for certain exponential cases, such as T=Th(Ran,exp).