This paper deals with the following types of problems: Assume a Banach space
X has some property (P). Can it be embedded into some Banach space Z with a
finite dimensional decomposition having property (P), or more generally, having
a property related to (P)? Secondly, given a class of Banach spaces, does there
exist a Banach space in this class, or in a closely related one, which is
universal for this class?Comment: 26 page