Submission date: 22 April 2021

Abstract:

Let T be a polynomially bounded o-minimal theory extending the theory of real closed ordered fields. Let K be a model of T equipped with a T-convex valuation ring and a T-derivation. If this derivation is continuous with respect to the valuation topology, then we call K a T-convex T-differential field. We show that every T-convex T-differential field has an immediate strict T-convex T-differential field extension which is spherically complete. In some important cases, the assumption of polynomial boundedness can be relaxed to power boundedness.

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

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Full text arXiv 2104.10802: pdf, ps.