Uniform properties of rigid subanalytic sets

In the context of rigid analytic spaces over a non-Archimedean valued field, a rigid subanalytic set is a Boolean combination of images of rigid analytic maps. We give an analytic quanti. er elimination theorem for ( complete) algebraically closed valued fields that is independent of the field; in particular, the analytic quanti. er elimination is independent of the valued field's characteristic, residue field and value group, in close analogy to the algebraic case. This provides uniformity results about rigid subanalytic sets. We obtain uniform versions of smooth strati. cation for subanalytic sets and the Lojasiewicz inequalities, as well as a unfiorm description of the closure of a rigid semianalytic set.