User blog comment:Pellucidar12/Attempt at a FGH related notation/@comment-28606698-20170415185346/@comment-30754445-20170416092254

Is it at all possible to write fundamental sequences to all ordinals up to (and not including) ωck in a recursive notation?

Seems to me that the answer is no. The ordinal structure becomes more and more complex ad infintum and there doesn't seem to be any way to streamline the process.

So if my analysis is correct, the very "invoking" of ωck into an otherwise recursive notation is guranteed to result in a gap. Pellucidar's "failure" to supply the fundamental sequences is due to the fact that it is logically impossible to do so.