  Some intuitionistic set theories satisfy certain “hallmark” metamathematical properties, such as the disjunction and the existence properties. They can also be shown to be consistent with the addition of principles which go beyond what we most typically consider constructive. Among these are, for example, Church Thesis and Markov’s principle. For a description of these principles in the context of intuitionistic logic, the reader may wish to consult sections 4.2 and 5.2 of the entry on intuitionistic logic or Troelstra and van Dalen’s book Constructivism in Mathematics (Troelstra and van Dalen 1988).