Model Theory Seminar - Nigel Pynn-Coates - Monotone T-convex T-differential fields
Speaker: Nigel Pynn-Coates (Ohio State University)
Title: Monotone T-convex T-differential fields
Abstract:Let T be acomplete, model complete, power bounded o-minimal theory extending the theoryof real closed fields. A T-convex T-differential field is an expansion of amodel of T by a valuation and a derivation, each of which is compatible withthe o-minimal structure, the former in the T-convex sense of van denDries--Lewenberg and the latter in the sense of Fornasiero--Kaplan. When T isthe theory of the real field with restricted analytic functions, we can expandan ordered differential Hahn field to a T-convex T-differential field, in whichcase the derivation is monotone, i.e., weakly contractive with respect to the valuation (monotone differential Hahn fields were studied earlier by Scanlon andHakobyan). I will describe joint ongoing work with Kaplan on monotone T-convex T-differential fields, achieving among other results anAx--Kochen/Ershov type theorem for such structures. A key step is isolating anappropriate analogue of henselianity in this setting.
Location: HH 410