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arXiv · 1702.08281

Abstract elementary classes stable in $\aleph_0$

Saharon Shelah·Sebastien Vasey
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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). Assuming a locality property for types, we prove that such classes exhibit superstable-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 $\aleph_1$. We also give a supersimplicity condition under which the locality hypothesis follows from the rest.

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Saharon Shelah, Sebastien Vasey. 2017-02-27. Abstract elementary classes stable in $\aleph_0$. https://doi.org/10.1016/j.apal.2018.02.004

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