Proof-theoretic strength of Agda
Agda is a predicative type theory, so has a surprisingly low bound on its proof-theoretic strength. Things are a bit complicated because of some tricky level features, but if we ignore that, then a decent ordinal bound on it is the
References
- The strength of some Martin-Löf type theories
- Proof Theory of Martin-Löf Type Theory – An Overview
- https://archive.is/6MB4t
- https://cstheory.stackexchange.com/questions/32859/logical-reations-for-an-impredicative-system-in-a-predicative-metatheory
- https://cstheory.stackexchange.com/questions/48562/strongly-normalizing-type-theory-beyond-induction-recursion