Transferring saturation, the finite cover property, and stability

Saturation is (mu, kappa)-transferable in T if and only if there is an expa nsion T-1 of T with \T\ = \T\ such that if M is a mu-saturared model of T-1 and \M\ greater than or equal to kappa then the reduct M/L(T) is -saturate d. We characterize theories which are superstable without f.c.p.. or withou t f.c.p. as, respectively those where saturation is (N-0, lambda)-transfera ble or (kappa(T), lambda)-transferable for all lambda. Further if for some mu greater than or equal to \T\,2(mu) > mu(+), stability is equivalent to f o. all mu greater than or equal to \T\, saturation is (mu, 2(mu))-transfera ble.