  A Banach space contains either a minimal subspace or a continuum of
incomparable subspaces. General structure results for analytic equivalence
relations are applied in the context of Banach spaces to show that if $E_0$
does not reduce to isomorphism of the subspaces of a space, in particular, if
the subspaces of the space admit a classification up to isomorphism by real
numbers, then any subspace with an unconditional basis is isomorphic to its
square and hyperplanes and has an isomorphically homogeneous subsequence.
