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2 results

  • THE GROUP CONFIGURATION THEOREM FOR GENERICALLY STABLE TYPES

  • Part of
  • PAUL WANG
  • Journal:
    The Journal of Symbolic Logic , First View
    Published online by Cambridge University Press:
    11 November 2024, pp. 1-44
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  • We generalize Hrushovski’s group configuration theorem to the case where the type of the configuration is generically stable, without assuming tameness of the ambient theory. The properties of generically stable types, which we recall in the second section, enable us to adapt the proof known in the stable context.

  • Group configurations and germs in simple theories

  • Itay Ben-Yaacov
  • Journal:
    The Journal of Symbolic Logic / Volume 67 / Issue 4 / December 2002
    Published online by Cambridge University Press:
    12 March 2014, pp. 1581-1600
    Print publication:
    December 2002

  • We develop the theory of germs of generic functions in simple theories. Starting with an algebraic quadrangle (or other similar hypotheses), we obtain an “almost” generic group chunk, where the product is defined up to a bounded number of possible values. This is the first step towards the proof of the group configuration theorem for simple theories, which is completed in [3].