Answer to this questions shows that fast growing hierarchies can grow arbitrarily fast for some definition of 'arbitrary'.

Can second order arithmetic define all these functions (for any ordinal) and prove them as total?

Can higher order arithmetic define total functions that are undefinable in second order?

Is there a survey article on these and similar questions?


Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.