Abstract

$\underline{\text{Saturation is} -\text{transferable in} T}$ if and only if there is an expansion T$_1$ of T with $\mid T_1 \mid$ = $\mid T \mid$ such that if M is a $\mu$-saturated model of T$_1$ and $\mid M \mid \geq \kappa$ then the reduct M $\mid L$ is $\kappa$-saturated. We characterize theories which are superstable without f.c.p., or without f.c.p. as, respectively those where saturation is - transferable or, \lambda$)-transferable for all $\lambda$. Further if for some $\mu \geq \mid T \mid, 2^\mu > \mu^+$, stability is equivalent to for all $\mu \geq \mid T \mid$, saturation is - transferable.