User blog comment:Edwin Shade/Rank-on-Rank Turing Ordinals and Beyond/@comment-1605058-20180119225409/@comment-32876686-20180120015527

To address your points:


 * \(f_{\alpha}(n)\) matches \(f(n)\) iff \(f_{\alpha-1}(n)\leq^*f(n)<^*f_{\alpha+1}(n)\) where \(a(n)<^*b(n)\) indicates eventual domination of \(b(n)\) over \(a(n)\) and \(a(n)\leq^*b(n)\) indicates either both functions \(a(n)\) and \(b(n)\) have equal growth rates or \(a(n)<^*b(n)\) as before. I am aware the wording in the blog was not very precise.


 * I'm not sure I understand the post entirely, as they do not make mention of the Church-Kleene ordinal.


 * I do not understand what you are trying to say here. Perhaps rephrasing yourself would be to my benefit.


 * Level\(\alpha\) Turing machines are as defined in this Wiki's article on the busy beaver function, when oracle Turing machines are being discussed. To me extending oracle levels to transfinite ordinals is rather simple but if you can explain the inequivalent things you speak of then I can learn more about this matter.