User blog comment:PsiCubed2/My attempt for creating an ψ(ψᵢ(0))-level notation for ordinals/@comment-39162-20170404170110/@comment-28606698-20170404210809

I would added somewhat:

$$\psi_\Iota(\alpha+1)[0]=\psi_\Iota(\alpha)+1$$,

$$\psi_\Iota(\alpha+1)[n+1]=\Omega_{\psi_\Iota(\alpha+1)[n]}$$,

$$\psi_\Iota(\alpha)[n]=\psi_\Iota(\alpha[n])$$ если $$\alpha$$ предельный ординал,

$$\psi_\Iota(\Iota)[n+1]=\psi_\Iota(\psi_\Iota(\Iota)[n])$$,

$$\varepsilon_{\Iota+1}[n+1]=\Iota^{\varepsilon_{\Iota+1}[n]}$$.