Intensional models for the theory of types

  title={Intensional models for the theory of types},
  author={Reinhard Muskens},
  journal={J. Symb. Log.},
In this paper we define intensional models for the classical theory of types, thus arriving at an intensional type logic ITL. Intensional models generalize Henkin’s general models and have a natural definition. As a class they do not validate the axiom of Extensionality. We give a cut-free sequent calculus for type theory and show completeness of this calculus with respect to the class of intensional models via a model existence theorem. After this we turn our attention to applications. Firstly… CONTINUE READING


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