Stratifications and term description over valued fields with analytic structure, uniform Yomdin-Gromov parametrizations

Abstract: We establish a certain strong smooth stratification of sets and a term description of functions, which are definable over valued fields (possibly non algebraically closed) with separated analytic structure. The basic tools are: elimination of valued field quantifiers, term structure of definable functions, Lipschitz cell decomposition with preparation of $RV$-parametrized sets, and a non-Archimedean definable version of Bierstone-Milman's canonical desingularization algorithm, achieved in an earlier paper of ours. As application, we give uniform Yomdin-Gromov parametrizations over Henselian fields $K$ with separated analytic structure.