User blog comment:Tetramur/My thoughts about functions and numbers/@comment-35470197-20191229115044/@comment-35470197-20191229153559

> There is one problem: the limit of admissible ordinals can be non-admissible.

What is the problem? I am not saying that ω_α^{CK} is defined as the α-th admissible one. For example, ω_1^{CK} not the first admissible ordinal ω.

> And one question: does the Kleene's O system give us a clue about the fundamental sequence of first CK ordinal?

Why not? If you have a problem on the definition of the canonical system of fundamental sequences, please tell me it explicitly.