User blog:Alejandro Magno/Extension of the Alphabet Hierarchy

Here is my extension.

Up to gamma(0)
a&<2>[A](x) = a&<1>[&<1>[&<1>[...[&<1>[&<1>[A]]]...]]](x) with x levels

a&[A](x) = a&[&[&[...[&[&[A]]]...]]](x) with x levels

a&[A](x) = a&[A](x)

etc.

FGH
a&<2>[A](x) = z(0)

a&<3>[A](x) = eta(0)

a&[A](x) = phi(w,0)

a&<&[A]>[A](x) = phi(w^w,0)

a&<&<1>[A]>[A](x) = phi(e(0),0)

a&<&[A]>[A](x) = phi(phi(w,0),0)

So the limit is gamma(0)

Up to SVO
-- UNDER CONSTRUCTION --