  It is shown that a script L_infty-space with separable dual constructed by
Bourgain and Delbaen has small Szlenk index and thus does not have a quotient
isomorphic to C(omega^omega). It follows that this is a script L_infty-space
which is the same size as c_0 in the sense of the Szlenk index but does not
contain c_0. This has some consequences in the theory of uniform homeomorphism
of Banach spaces.
