Transferring saturation, the finite cover property, and stability
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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 M is a mu-saturated model of T_1 and |M| \geq kappa then the reduct M|L(T) is kappa-saturated. We characterize theories which are superstable without the finite cover property (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 \geq |T|, 2^mu > mu^+, stability is equivalent to: or all mu \geq |T|, saturation is (μ,2^mu)-transferable.
This version replaces the 1995 submission: Characterization of the finite cover property and stability. This version submitted by John T. Baldwin. The paper has been accepted for the Journal of Symbolic Logic
This version replaces the 1995 submission: Characterization of the finite cover property and stability. This version submitted by John T. Baldwin. The paper has been accepted for the Journal of Symbolic Logic