Transferring saturation, the finite cover property, and stability

Details Transferring saturation, the finite cover property, and stability Transferring saturation, the finite cover property, and stability

1995-11-30

arxiv.org/abs/math/9511205v3

Mathematics

Logic

This version replaces the 1995 submission: Characterization of the finite cover property and stability. This version submitted

Scientific paper

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 (\mu,2^mu)-transferable.

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