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.
Original language | English |
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Pages (from-to) | 565-587 |
Number of pages | 23 |
Journal | Annals of Pure and Applied Logic |
Volume | 169 |
Issue number | 7 |
DOIs | |
State | Published - Jul 2018 |
Bibliographical note
Publisher Copyright:© 2018 Elsevier B.V.
Keywords
- Abstract elementary classes
- Good frames
- Locality
- Superlimit
- ℵ-stability