Article ID Journal Published Year Pages File Type
8904283 Annals of Pure and Applied Logic 2018 23 Pages PDF
Abstract
We study abstract elementary classes (AECs) that, in ℵ0, 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 ℵ0. More precisely, there is a superlimit model of cardinality ℵ0 and the class generated by this superlimit has a type-full good ℵ0-frame (a local notion of nonforking independence) and a superlimit model of cardinality ℵ1. We also give a supersimplicity condition under which the locality hypothesis follows from the rest.
Related Topics
Physical Sciences and Engineering Mathematics Logic
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