User blog comment:Deedlit11/Ordinal Notations V: Up to a weakly Mahlo cardinal/@comment-5029411-20130811125215/@comment-5150073-20140621070801

More possibilities:

I(2) = {w, w*2, w*3, ...}

I(2) = {w, w^2, w^3, ...}

I(2) = {e_0, e_1, e_2, ...}

I(2) = {z_0, z_1, z_2, ...}

I(2) = {$$\Omega_1, \Omega_2, \Omega_3$$, ...}

We're free to choose it.