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Creators/Authors contains: "Pynn-Coates, Nigel"

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  1. ; (, Model Theory)
    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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    Free, publicly-accessible full text available January 22, 2026