journal contribution posted on 09.11.2015, 00:00 by JT Baldwin, PB Larson, S. Shelah
Theorem. Suppose that an @0-presentable Abstract Elementary Class (AEC),K, has the joint embedding and amalgamation properties in @0 and < 2@1 models in @1. If K has only countably many models in @1, then all are small. If, in addition, K is almost Galois !-stable then K is Galois !-stable.
Research partially supported by Simons travel grant G5402
Supported in part by NSF Grant DMS-0801009.
Research partially supported by NSF grant no: DMS 1101597, and German-Israeli Foundation for Scientific Research & Development grant no. 963-98.6/2007. Publication number 1003. Part of f1179 on the Shelah Archive.
Publisher StatementThis is the copy of an article published in the Journal of Symbolic Logic © 2015 Association for Symbolic Logic Publications.
PublisherAssociation for Symbolic Logic