Abstract

We give two nite axiomatizations of indexed inductive-recursive de nitions in intuitionistic type theory. They extend our previous nite axiomatizations of inductive-recursive de nitions of sets to indexed families of sets and encompass virtually all de nitions of sets which have been used in intuitionistic type theory. The more restricted of the two axiomatization arises naturally by considering indexed inductive-recursive de nitions as initial algebras in slice categories, whereas the other admits a more general and convenient form of an introduction rule.

Citations