User blog comment:Wythagoras/All my stuff/@comment-5029411-20130716190012

5 Rule FGH to reach theta(Omega^Omega):

f0(a) = a+1

f@+1(a) = f@^a(a)

f@w^(@+1)*b+1(a) = f@w^(@+1)*b+w^@(a)

f@phi(@ @+1,@+1)(a) = f@phi(@ @,phi...(@ @,phi(@ @+1,@)+1)...)(a) (a+1 phi's)

f@phi(@ @+1,0,0...0,@+1)(a) = f@phi(@ @,phi(@ @,...phi(@ @,phi(@ @,phi(@ @,0,0...0,@),0...0,1),0...0,0)...,0...0,0),0...0,0)(a) (a+1 phi's)

f@theta(@ Omega^(@+1)*(@+1))(a) = f@theta(@ Omega^(@+1)*@+theta(@ Omega^(@+1)*@+...theta(@ Omega^(@+1)*@+theta(@ Omega^(@+1)*@))))(a) (a theta's)

Y(6) = ftheta(Omega^Omega)(6)