Submission date: 31 January 2022

Abstract:

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

Mathematics Subject Classification: Primary 03C64, Secondary 12H05, 12J10

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Full text arXiv 2201.13258: pdf, ps.