Submission date: 25 September 2023

Abstract:

Let T be a complete, model complete o-minimal theory extending the theory of real closed ordered fields and assume that T is power bounded. Let K be a model of T equipped with a T-convex valuation ring 𝒪 and a T-derivation ∂ such that ∂ is monotone, i.e., weakly contractive with respect to the valuation induced by 𝒪. We show that the theory of monotone T-convex T-differential fields, i.e., the common theory of such K, has a model completion, which is complete and distal. Among the axioms of this model completion, we isolate an analogue of henselianity that we call T^∂-henselianity. We establish an Ax-Kochen/Ershov theorem and further results for monotone T-convex T-differential fields that are T^∂-henselian.

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Full text arXiv 2309.13951: pdf, ps).