  We prove that if X is a separable infinite dimensional Banach space then its
isomorphism class has infinite diameter with respect to the Banach-Mazur
distance. One step in the proof is to show that if X is elastic then X contains
an isomorph of c_0. We call X elastic if for some K < infinity for every Banach
space Y which embeds into X, the space Y is K-isomorphic to a subspace of X. We
also prove that if X is a separable Banach space such that for some K <
infinity every isomorph of X is K-elastic then X is finite dimensional.
