A finite axiomatisation of inductive-inductive definitions
نویسندگان
چکیده
Induction-induction is a principle for mutually defining data types A ∶ Set and B ∶ A→ Set. Both A and B are defined inductively, and the constructors for A can refer to B and vice versa. In addition, the constructor for B can refer to the constructor for A. Induction-induction occurs in a natural way when formalising dependent type theory in type theory. We give some examples of inductive-inductive definitions, such as the set of surreal numbers. We then give a new finite axiomatisation of the principle of induction-induction, and prove its consistency by constructing a model.
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