User blog comment:Wythagoras/FGH Dollars Function/@comment-5529393-20130710150026

Why do you have [0, [0,1]_2 ] ~ psi(Omega^(Omega+1))?

You have

[0, 1] ~ Gamma_0

[0, 2] ~ Gamma_1

[0, [0]] ~ Gamma_w

The pattern is that [0, 1 + X] ~ Gamma_X. So

[0, [0,1]] ~ Gamma_Gamma_0

[0, [0,1]_2 ] ~ Gamma_(epsilon_(Gamma_0 + 1))

[0, [0,1]_[0] ] ~ Gamma_(phi(w, Gamma_0 + 1))

[0, [0,1]_[0,1] ] ~ Gamma_(phi(Gamma_0, 1))

[0, [0,2]] ~ Gamma_(Gamma_1)

[0, [0, [0, 1]] ~ Gamma_Gamma_Gamma_0

[0, 0, 1] ~ phi (1, 1, 0)

My belief is that the strength of Linear Array Notation is the Small Veblen Ordinal.