Abstract elementary classes stable in ℵ0

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Abstract

We study abstract elementary classes (AECs) that, in 0, 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 0. More precisely, there is a superlimit model of cardinality 0 and the class generated by this superlimit has a type-full good 0-frame (a local notion of nonforking independence) and a superlimit model of cardinality 1. We also give a supersimplicity condition under which the locality hypothesis follows from the rest.

MSC

primary
03C48
secondary
03C45
03C55
03C75

Keywords

Abstract elementary classes
0-stability
Good frames
Superlimit
Locality

Cited by (0)

The first author would like to thank the Israel Science Foundation for partial support of this research (Grant No. 242/03). Research partially supported by European Research Council grant 338821, and by National Science Foundation grant no: 136974. 1119 on Shelah's publication list.

1

Current address: Department of Mathematics, Harvard University, Cambridge, Massachusetts, USA.