User blog comment:Nayuta Ito/faketest/e0/@comment-30754445-20180804174000/@comment-30754445-20180804224527

You probably meant:

U(W_2+U_1(W_2+1))

And we already know that that ordinal is equal to ψ(εΩ+1ω) (this one is actually written explicitly).

(and what you've actually written is even smaller, because U(W_2+1) is less than W)

Are you sure about this system being simple and intuitive? ;-)