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1 results

  • Definability of groups in ℵ0-stable metric structures

  • Itaï Ben Yaacov
  • Journal:
    The Journal of Symbolic Logic / Volume 75 / Issue 3 / September 2010
    Published online by Cambridge University Press:
    12 March 2014, pp. 817-840
    Print publication:
    September 2010

  • We prove that in a continuous ℵ0-stable theory every type-definable group is definable. The two main ingredients in the proof are:

    (i) Results concerning Morley ranks (i.e., Cantor-Bendixson ranks) from [Ben08], allowing us to prove the theorem in case the metric is invariant under the group action; and

    (ii) Results concerning the existence of translation-invariant definable metrics on type-definable groups and the extension of partial definable metrics to total ones.