Definable Functions and Stratifications in Power-Bounded T -Convex Fields

Abstract

We study properties of definable sets and functions in power-bounded $T$-convex fields, proving that the latter have the multidimensional Jacobian property and that the theory of $T$-convex fields is $b$-minimal with centers. Through these results and work of I. Halupczok we ensure that a certain kind of geometrical stratifications exist for definable objects in said fields. We then discuss a number of applications of those stratifications, including applications to Archimedean o-minimal geometry.