User blog comment:Alejandro Magno/SPECIAL! FGH of Hyperion Notation/@comment-24725252-20170722165352

Aarex's comparisons beyond (0[1]1) are wrong. The function is much stronger than Aarex's analysis showed.

(0,1[1]1)#n has level e(phi(w,0)+1)

(0[1]2)#n has level phi(w,1)

(0[1]0,1)#n has level phi(w+1,0)

(0[1]0[1]1)#n has level phi(w*2,0)

(0[2]n)#n has level phi(w^2,0)

(0[(0)]n)#n has level phi(w^w,0)

(0[(0)]n)#n has level phi(w^w,0)

(0[0,1]1)#n has level gamma(0)

(0[(0[0,1]1)]1[0,1]1)#n has level phi(gamma(0),1)

(0[0,1]2)#n has level gamma(1)

(0[0,1]0,1)#n has level phi(1,1,0)= psi(W^(W+1))

(0[0,1]0[0,1]1)#n has level phi(2,0,0)= psi(W^(W*2))

(0[0,2]1)#n has level phi(1,0,0,0)= psi(W^(W^2))

(0[0,(0)]1)#n has level SVO = psi(W^(W^w))

(0[0,0,1]1)#n has level LVO = psi(W^(W^W))

(0[0,1,1]1)#n has level psi(W^(W^(W+1)))

(0[0,0,2]1)#n has level psi(W^(W^(W*2)))

(0[0,0,0,1]1)#n has level psi(W^(W^(W^2)))

(0[0[1]1]1)#n has level psi(W^(W^(W^w)))

(0[0[0,1]1]1)#n has level psi(W^(W^(W^W)))

(0[0[0,1]2]1)#n has level psi(W^(W^(W^W*2)))

(0[0[0,1]0[0,1]1]1)#n has level psi(W^(W^(W^(W*2))))

(0[0[0,2]1]1)#n has level psi(W^(W^(W^(W^2))))

(0[0[0,0,1]1]1)#n has level psi(W^(W^(W^(W^W))))

(0[0[0[0,1]1]1]1)#n has level psi(W^W^W^W^W^W)

(0,11)#n has level BHO