User blog comment:Ubersketch/Do hypernomials reach CK?/@comment-35470197-20190610224405

The question does not make sense unless you specify the explicit definitions which you used. For example, you just "explained" how erdinals works and are different from ordinals, but have not defined the notion. Also, you have not declared what kind of strings which you allow to use. At least, if you allow all functions, e.g. \(f_{\omega_1^{\textrm{CK}}}\), the resulting notation consists of uncountably many terms. Also, your definition of the order does not give a well-ordering, and hence it is ambiguous what "reach CK" means.