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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: Ea+1(n) = Ea(n)<0<P(n)<1>>1> (Using TaN)

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

Salvation rule: m+1E0(n) = mE(FOOST(10^n))(n)

Rule rule: 0E(n) = E(FOOST(10^n))(n)

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 and a system of fundamental sequences that goes up to that ordinal and covers all smaller ordinals (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.

Calculating a couple of examples

E1(2) =  E0(2)<0<P(n)<1>>1> = )2(<0<P(n)<1>>1> (Pretty big)

E2(2) =  E1(2)<0<P(n)<1>>1> (Bigger)

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