Submission date: 21 April 2017

Abstract:

We show that functions definable in power bounded T-convex fields have the (multidimensional) Jacobian property. Building on work of I. Halupczok, this implies that a certain notion of non-archimedean stratifications is available in such valued fields. From the existence of these stratifications, we derive some applications in an archimedean o-minimal setting. As a minor result, we also show that if T is power bounded, the theory of T-convex valued fields is b-minimal with centres.

Mathematics Subject Classification: 03C98, 03C64, 14P99

Keywords and phrases:

Full text arXiv 1704.06558: pdf, ps.