User blog comment:Alemagno12/An extremely fast-growing OCF/@comment-5029411-20170726203426/@comment-5029411-20170726215946

No, $$\psi\text{L}_{L(\omega)}(n)$$ is same as nth term of $$L(\omega)$$, however ωth is self-identity term of $$L(\omega)$$.

The results of $$L$$ well-definedness is ill-definedness.