Abstract elementary classes stable in ℵ0

Saharon Shelah, Sebastien Vasey*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

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 languageEnglish
Pages (from-to)565-587
Number of pages23
JournalAnnals of Pure and Applied Logic
Volume169
Issue number7
DOIs
StatePublished - Jul 2018

Bibliographical note

Publisher Copyright:
© 2018 Elsevier B.V.

Keywords

  • Abstract elementary classes
  • Good frames
  • Locality
  • Superlimit
  • ℵ-stability

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