Sh:570

• Baldwin, J. T., Grossberg, R. P., & Shelah, S. (1999). Transfering saturation, the finite cover property, and stability. J. Symbolic Logic, 64(2), 678–684. arXiv: math/9511205 DOI: 10.2307/2586492 MR: 1777778
• 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\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\geq |T|, 2^\mu>\mu^+, stability is equivalent to for all \mu\geq |T|, saturation is (\mu,2^\mu)-transferable.
• Version 1997-11-25_10 (11p) published version (8p)

@article{Sh:570,
 author = {Baldwin, John T. and Grossberg, Rami P. and Shelah, Saharon},
 title = {{Transfering saturation, the finite cover property, and stability}},
 journal = {J. Symbolic Logic},
 fjournal = {The Journal of Symbolic Logic},
 volume = {64},
 number = {2},
 year = {1999},
 pages = {678--684},
 issn = {0022-4812},
 mrnumber = {1777778},
 mrclass = {03C45 (03C50)},
 doi = {10.2307/2586492},
 note = {\href{https://arxiv.org/abs/math/9511205}{arXiv: math/9511205}},
 arxiv_number = {math/9511205}
}