User blog comment:Alemagno12/I made a Pi w-reflection OCF, how horribly wrong am I?/@comment-35470197-20180812220655/@comment-35470197-20180813023451

> However, we can easily define an FS system for the OCF by defining the complexity of expressions expressible using the OCF:

I asked the question in order to know whether there is a way to define an ordina notation associated to it or not. Such a expression-based technique is not useful in this case, because we do not have \(\alpha = \sup_{n < \omega} \alpha[n]\) in general with respect to the FS you defined.

Sorry for the ambiguity of the question.