Classes Stable in א 0
نویسنده
چکیده
ELEMENTARY CLASSES STABLE IN א0 SAHARON SHELAH AND SEBASTIEN VASEY 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). 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. This extends the first author’s earlier study of PCא0 -representable AECs and also improves results of HyttinenKesälä and Baldwin-Kueker-VanDieren. 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). 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. This extends the first author’s earlier study of PCא0 -representable AECs and also improves results of HyttinenKesälä and Baldwin-Kueker-VanDieren.
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