User blog:KthulhuHimself/VAST function

Time for another computable function!

The VAST function (notated E[a](n), with a being an ordinal) is a two-variable computable extension to Plexation, that is immensely stronger than most computable functions, if not all of them, to date.

Etymology
VAST function stands for Very-Awesome-Super-Tremendous function, and is called so based of the principle of yolo.

Go figure.

Defenition
Definition is simple:

Base rule: E0(n) = )n(  (Plexation)

Successor rule:  E a+1 (n) =  E a n (n)

Limit rule:  E a (n) =  E a[n] (n)  If and only if a is a limit ordinal

Seems familiar?

Quick conclusion
Obviously, this function is comparable to the FGH itself, and so keeps up with it as long as limit ordinals are defined, making it meaningfully strong.

Number!
Hyperkthulhu = EΨ(ψᵢ(0)) (5,000)

Quite big, if I may say so myself.

Extension into a one-variable, uncomputable function
Define an alternate version of Rayo(n) (We'll call it FOOST(n)), which instead of generating the largest finite number with n symbols, will generate the largest recursive ordinal with them ( An ordinal is considered  recursive  iff it is the order type of a computable well-ordering of a subset of the natural numbers ).

Definition
E (n) =  E (FOOST(10^n)) (n)

Another number!
Ultrakthulhu =  E (5,000)

Even bigger.