User blog:MachineGunSuper/Graham Hierarchy

The Graham Hierarchy is a hierarchy for producing very deep graham nestings.

For the sake of this, we will represent the graham function with capital G

GH0(n) = Gn

Graham's Number = GH0(64)

'''GH1(n) = GG G. . . G n    , where there are GH0(n) G's'''

Eg: GH1(3) = GG G. . . G 3 , with G3 G's above 3

And surprisingly, this is all that we need to define, because no matter if n is a transfinite ordinal/a finite number, for n>1, GHn(x) = GHxn-1(x)

Basically, when the subscript is bigger than 1, you will just do the FGH style recursion and diagonalization.

So, when the subscript > 1,just work as if you had the FGH, just when you reach 1,0 in the subscript follow the rules listed above.

GH2(3) = GH1(GH1(GH1(3)))

GHω(n) = GHn(n) etc.

The question of the blog post
I already coined a number, called Graham's Gamma = GH\(\Gamma_0\)(64)

You try seeing how big it is and where it would stand in the classes of the wiki.