Functorial Fast-Growing Hierarchies

Functorial Fast-Growing Hierarchies

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We prove an isomorphism theorem between the canonical denotation systems for simply southern cat shirt large natural numbers and large countable ordinal numbers, linking two fundamental concepts in Proof Theory.The first one is fast-growing hierarchies.These are sequences of functions on $mathbb {N}$ obtained through processes such as the ones that yield multiplication from addition, exponentiation from multiplication, etc.and represent the canonical way of speaking simply boho classroom about large finite numbers.

The second one is ordinal collapsing functions, which represent the best-known method of describing large computable ordinals.