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Keywords:

  • The independence property;
  • stability;
  • dependent theories;
  • MSC (2010) 03C07;
  • 03C45;
  • 03C64

Abstract

A theory is stable up to Δ if any Δ-type over a model has a few extensions up to complete types. We prove that a theory has no the independence property iff it is stable up to some Δ, where each equation image has no the independence property.