We show that any Banach space contains a continuum of non isomorphic subspaces or a minimal subspace. We define an ergodic Banach space X as a space such that E0 Borel reduces to isomorphism on the set of subspaces of X, and show that every Banach space is either ergodic or contains a subspace with an unconditional basis whichiscomplementablyuniversalforthefamilyofitsblock−subspaces.Wealsouseourmethodstogetuniformityresults;forexample,incombinationwitharesultofB.Maurey,V.MilmanandN.Tomczak−Jaegermann,weshowthatanunconditionalbasisofaBanachspace,ofwhicheveryblock−subspaceiscomplemented,mustbeasymptoticallyc_0orl_p$.
