Published online by Cambridge University Press: 12 March 2014
Saturation is (μ, κ)-transferable in T if and only if there is an expansion T 1 of T with |T 1| = |T| such that if M is a μ-saturated model of T 1 and |M| ≥ κ then the reduct M|L(T) is κ-saturated. We characterize theories which are superstable without f.c.p., or without f.c.p. as, respectively those where saturation is (ℵ0, λ)-transferable or (κ(T), λ)-transferable for all λ. Further if for some μ ≥ |T|,2 μ > μ +, stability is equivalent to for all μ ≥ |T|, saturation is (μ, 2 μ )-transferable.
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