User blog comment:Wythagoras/Dollar function formal definition/@comment-5150073-20130629110623/@comment-5529393-20130630010631

The standard ordinal notation at this level uses an inaccessible cardinal I. lambda (a, b) would be represented as psi_I (Ia + b), and lambda_a (b, c) would be represented as psi_I (I^2 a + I b + c). The notation can go to psi_I (Gamma_{I + 1}) or higher.

The strength of D(n) is much higher than this, and higher than any explicit notation yet devised, even though they get _very_ strong and complicated.