User blog comment:Deedlit11/Ordinal Notations IV: Up to a weakly inaccessible cardinal/@comment-1605058-20130709080441/@comment-5529393-20130709085952

The largest countable ordinal expressible in the notation will be the limit of $$\psi_{\Omega_1}(I+1), \psi_{\Omega_1}(\Omega_{I+1}), \psi_{\Omega_1}(\Omega_{\Omega_{I+1}}), \psi_{\Omega_1}(\Omega_{\Omega_{\Omega_{I+1}}}), \ldots$$