Definable functions and stratifications in power-bounded \(T\)-convex fields (Q2656213)

T-stratification for henselian valued fields of equi-characteristic zero is defined, and a sufficient condition for valued fields admitting t-stratification is provided in [\textit{I. Halupczok}, Proc. London Math. Soc. 109, 1304--1362 (2014; Zbl 1382.03061)]. This paper demonstrates that \(T\)-convex fields given in [\textit{L. van den Dries} et al., J. Symbolic Logic 60, 74--102 (1995; Zbl 0856.03028)] satisfy the sufficient condition when \(T\) is a power-bounded complete o-minimal theory extending the theory of real closed fields. It also demonstrates that \(T\)-convex field does not admit t-stratification when the exponentiation is definable.