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1 results

  • DECIDABLE MODELS OF ω-STABLE THEORIES

  • URI ANDREWS
  • Journal:
    The Journal of Symbolic Logic / Volume 79 / Issue 1 / March 2014
    Published online by Cambridge University Press:
    17 April 2014, pp. 186-192
    Print publication:
    March 2014

  • We characterize the ω-stable theories all of whose countable models admit decidable presentations. In particular, we show that for a countable ω-stable T, every countable model of T admits a decidable presentation if and only if all n-types in T are recursive and T has only countably many countable models. We further characterize the decidable models of ω-stable theories with countably many countable models as those which realize only recursive types.