We study properties of definable sets and functions in power-bounded -convex fields, proving that the latter have the multidimensional Jacobian property and that the theory of -convex fields is -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.
"Definable Functions and Stratifications in Power-Bounded -Convex Fields." Notre Dame J. Formal Logic 61 (3) 441 - 465, September 2020. https://doi.org/10.1215/00294527-2020-0013