User blog comment:Naruyoko/My Tottaly Not Broken "Ordinal Notation", Which Totally is Well-Defined and Covers All Ordinals To the Limit Ok Why Is the Title so Long/@comment-35470197-20190318222152

It is totally ill-defined because you have not defined a primitive recursive relation \(<\).

Also, \(t(\ldots) = \omega\) does not make sense because an ordinal notation only allows expressions of finite length. So the limit of your notation is \(\omega\).