### Transfering saturation, the finite cover property, and stability

by Baldwin and Grossberg and Shelah. [BGSh:570]

J Symbolic Logic, 2000

Saturation is (mu, kappa)-transferable in T if and only if
there is an expansion T_1 of T with |T_1|=|T| such that if Mis a mu-saturated model of T_1 and |M| >= kappa then the
reduct M restriction L(T) is kappa-saturated. We characterize
theories which are superstable without f.c.p., or without f.c.p.
as, respectively those where saturation is
(aleph_0, lambda)-transferable or
(kappa (T), lambda)-transferable for all lambda . Further if for
some mu >= |T|, 2^mu > mu^+, stability is equivalent to for
all mu >= |T|, saturation is (mu,2^mu)-transferable.

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