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1 results

  • FORKING AND SUPERSTABILITY IN TAME AECS

  • SEBASTIEN VASEY
  • Journal:
    The Journal of Symbolic Logic / Volume 81 / Issue 1 / March 2016
    Published online by Cambridge University Press:
    09 March 2016, pp. 357-383
    Print publication:
    March 2016
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  • 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.