Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.
Q&A for work
Connect and share knowledge within a single location that is structured and easy to search.
Are there known type theories in the literature, which have strong normalization proofs and their proof-theoretical strength goes beyond strength of type theories with induction-recursion?
Yes. System F is probably the simplest example. As far as I know, you can’t prove normalisation for it in a dependent type theory with induction-recursion — you need at least impredicative prop to do so.
Required, but never shown