2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/129864For a countable ordinal a we denote by C_a the class of separable, reflexive Banach spaces whose Szlenk index and the Szlenk index of their dual are bounded by a. We show that each C_a admits a separable, reflexive universal space. We also show that spaces in the class C_{omega^{a*omega}} embed into spaces of the same class with a basis. As a consequence we deduce that each C_a is analytic in the Effros-Borel structure of subspaces of C[0,1].29 pages, uses mypreamble.tex and szlenk.bblFunctional Analysis46B20 (Primary); 54H05 (Secondary)text