Sh:1119

• Shelah, S., & Vasey, S. (2018). Abstract elementary classes stable in \aleph_0. Ann. Pure Appl. Logic, 169(7), 565–587. arXiv: 1702.08281 DOI: 10.1016/j.apal.2018.02.004 MR: 3788738
• Abstract:
  We study abstract elementary classes (AECs) that, in \aleph_0, have amalgamation, joint embedding, no maximal models and are stable (in terms of the number of orbital types). We prove that such classes exhibit super stable-like behavior at \aleph_0. More precisely, there is a superlimit model of cardinality \aleph_0 and the class generated by this superlimit has a type-full good \aleph_0-frame (a local notion of nonforking independence) and a superlimit model of cardinality \aleph_1. This extends the first author’s earlier study of PC_{\aleph_0}-representable AECs and also improves results of Hyttinen-Kesala and Baldwin-Kueker-VanDieren.
• published version (23p)

@article{Sh:1119,
 author = {Shelah, Saharon and Vasey, Sebastien},
 title = {{Abstract elementary classes stable in $\aleph_0$}},
 journal = {Ann. Pure Appl. Logic},
 fjournal = {Annals of Pure and Applied Logic},
 volume = {169},
 number = {7},
 year = {2018},
 pages = {565--587},
 issn = {0168-0072},
 mrnumber = {3788738},
 mrclass = {03C48 (03C45 03C55 03C75)},
 doi = {10.1016/j.apal.2018.02.004},
 note = {\href{https://arxiv.org/abs/1702.08281}{arXiv: 1702.08281}},
 arxiv_number = {1702.08281}
}