Functorial Fast-Growing Hierarchies

Functorial Fast-Growing Hierarchies

Blog Article

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

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