Abstract elementary classes stable in $\aleph_0$
Logic
2018-05-31 v5
Abstract
We study abstract elementary classes (AECs) that, in , have amalgamation, joint embedding, no maximal models and are stable (in terms of the number of orbital types). Assuming a locality property for types, we prove that such classes exhibit superstable-like behavior at . More precisely, there is a superlimit model of cardinality and the class generated by this superlimit has a type-full good -frame (a local notion of nonforking independence) and a superlimit model of cardinality . We also give a supersimplicity condition under which the locality hypothesis follows from the rest.
Cite
@article{arxiv.1702.08281,
title = {Abstract elementary classes stable in $\aleph_0$},
author = {Saharon Shelah and Sebastien Vasey},
journal= {arXiv preprint arXiv:1702.08281},
year = {2018}
}
Comments
27 pages