Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8904283 | Annals of Pure and Applied Logic | 2018 | 23 Pages |
Abstract
We study abstract elementary classes (AECs) that, in âµ0, 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 âµ0. More precisely, there is a superlimit model of cardinality âµ0 and the class generated by this superlimit has a type-full good âµ0-frame (a local notion of nonforking independence) and a superlimit model of cardinality âµ1. We also give a supersimplicity condition under which the locality hypothesis follows from the rest.
Related Topics
Physical Sciences and Engineering
Mathematics
Logic
Authors
Saharon Shelah, Sebastien Vasey,