User blog comment:Ikosarakt1/Fast-growing hierarchy/@comment-78.22.170.27-20130619192628/@comment-1605058-20130625053426

Taranovsky's notation, if correct, may be important breakthrough. But according to Loader (et al.) functions computable by CoC are the same as provably recursive functions in HOL. As we know even second-order logic is much stronger than second-order arithmetic, gap is still extremelly large.