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Preprint Number 1173

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1173. Saharon Shelah, Sebastien Vasey
Abstract elementary classes stable in ℵ_0

Submission date: 27 February 2017


We study abstract elementary classes (AECs) that, in ℵ_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 superstable-like behavior at ℵ_0. More precisely, there is a superlimit model of cardinality ℵ_0 and the class generated by this superlimit has a type-full good ℵ_0-frame (a local notion of nonforking independence) and a superlimit model of cardinality ℵ_1. This extends the first author's earlier study of PC_{ℵ_0}-representable AECs and also improves results of Hyttinen-Kesälä and Baldwin-Kueker-VanDieren.

Mathematics Subject Classification: 03C48 (Primary), 03C45, 03C52, 03C55 (Secondary)

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Full text arXiv 1702.08281: pdf, ps.

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