Transferring saturation, the finite cover property, and stability
Abstract
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.
Keywords
Cite
@article{arxiv.math/9511205,
title = {Transferring saturation, the finite cover property, and stability},
author = {J. Baldwin and R. Grossberg and Saharon Shelah},
journal= {arXiv preprint arXiv:math/9511205},
year = {2008}
}
Comments
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