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Estimation of the Szlenk index of reflexive Banach spaces using generalized Baernstein spaces
For each ordinal $\alpha <\omega _1$, we prove the existence of a separable, reflexive Banach space $W$ with a basis so that $ {\rm Sz}(W), {\rm Sz}(W^*)\leq \omega ^{\alpha +1}$ which is universal for the class of separable, reflexive Banach spaces $X$