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FORKING AND SUPERSTABILITY IN TAME AECS

  • SEBASTIEN VASEY (a1)
Abstract
Abstract

We prove that any tame abstract elementary class categorical in a suitable cardinal has an eventually global good frame: a forking-like notion defined on all types of single elements. This gives the first known general construction of a good frame in ZFC. We show that we already obtain a well-behaved independence relation assuming only a superstability-like hypothesis instead of categoricity. These methods are applied to obtain an upward stability transfer theorem from categoricity and tameness, as well as new conditions for uniqueness of limit models.

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Monica VanDieren , Categoricity in abstract elementary classes with no maximal models. Annals of Pure and Applied Logic, vol. 141 (2006), pp. 108147.

Monica VanDieren , Erratum to “Categoricity in abstract elementary classes with no maximal models” [Ann. Pure Appl. Logic 141 (2006) 108-147]. Annals of Pure and Applied Logic, vol. 164 (2013), no. 2, pp. 131133.

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The Journal of Symbolic Logic
  • ISSN: 0022-4812
  • EISSN: 1943-5886
  • URL: /core/journals/journal-of-symbolic-logic
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