Transferring saturation, the finite cover property, and stability

1995/11/30 by J. Baldwin, Baldwin, J., R. Grossberg +3
Mathematics · #FOS: Mathematics #Logic (math.LO) #math.LO

paper · pdf · doi:10.48550/arxiv.math/9511205

published as J. Symbolic Logic 64 No. 2 (1999) 678--684 · 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

arxiv created 1998/07/09 · arxiv updated 2009/11/30

Abstract

Saturation is (mu,kappa)-transferable in T if and only if there is an expansion T₁ of T with |T₁| = |T| such that if M is a mu-saturated model of T₁ and |M| ≥ 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 (aleph₀,lambda)-transferable or (kappa(T),lambda)-transferable for all lambda. Further if for some mu ≥ |T|, 2^mu > mu⁺, stability is equivalent to: or all mu ≥ |T|, saturation is (μ,2^mu)-transferable.

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