Non-archimedean stratifications in power bounded $T$-convex fields

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.

References in corpus (2)

• Quantifier elimination and minimality conditions in algebraically closed valued fields
• Generalized Euler characteristic in power-bounded T-convex valued fields

Cited by in corpus (1)

• Hensel minimality I