# 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. - published version (8p)

Bib entry

@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}, doi = {10.2307/2586492}, mrclass = {03C45 (03C50)}, mrnumber = {1777778}, mrreviewer = {Fuxing Shen}, doi = {10.2307/2586492}, note = {\href{https://arxiv.org/abs/math/9511205}{arXiv: math/9511205}}, arxiv_number = {math/9511205} }