User blog:Alemagno12/An extremely fast-growing OCF

Sometimes, there are notations that are so strong that norrmal ordinal notation can't handle it. So I will make a new ordinal OCF, Ψa(b), and two functions to generate the uncountable ordinals used in the OCF, ΨLa(b) and L(x).

WIP!

What's an omega-limit ordinal?
We all know what sequence and limit ordinals are, but what's an omega-limit ordinal?

An omega-limit ordinal is the limit of a set of ordinals of the form ΨLL(a)(b), for a specific a. But it's not like a limit ordinal, like the relation ω has to the set of non-negative integers, it's more of like the relation that the first uncountable inaccesible cardinal has to the set of all alephx.

If an ordinal L(x) is the omega-limit of a set of ordinals of the form ΨLL(x)(b) for all b, then that ordinal is the smallest ordinal that does not belong to that set.

For example, L(ω) is the omega-limit of the sequence of ordinals ΨLL(ω)(x) for all b.