User blog comment:Wythagoras/Dollar function formal definition/@comment-5529393-20130616091711/@comment-5529393-20130616102343

I see. But, using the rule as described in your comment, I still don't think the notation works like you want it to.

We have

a$[0]_(1[0]) = a$[0]_[0] [0]_[0] ,,, [0]_[0] = f_{phi(omega, 0) + 1} (a).

Similarly, a$[0]_(b[0]) = f_{phi(omega, 0) + b} (a).

a$[0]_([0][0]) = f_{phi(omega, 0) + omega} (a).

a$[0]_([0][0][0]) = f_{phi(omega, 0) + omega*2} (a).

a$[0]_[1] = f_{phi(omega, 0) + omega^2} (a).

a$[0]_b = f_(phi(omega,0) + B) (a) where B is the ordinal associated with b.

a$[0]_[0]_[0] = f_{phi(omega, 0) + phi(omega,0)} (a).

a$[0,1] = f_{phi(omega, 0) * omega} (a), not f_Gamma_0 (a).