User blog:P進大好きbot/How to compute the cofinality of an ordinal number of a specific form

Hi! I would like to know how you creat so outstanding ordinal notations for googology.

For this purpose, I would like to know how you compute the cofinality of an ordinal of the form \(F_{\alpha}(\beta)\) for the OCF \((F_{\alpha})_{\alpha}\) which you have created to obtain an ordinal notation.

Of course, it depends on the definition of the OCF which you use, but I would like to know a general approach independent of the choice of the OCF.

For the use in googology, it might be better to assume \(\textrm{cof}(F_{\alpha}(\beta)) \in \{1,\omega,\textrm{cof}(\alpha),\textrm{\beta}\}\) (and also some reasonable continuity such as Scott continuity for a right variable). Is there any good general approach in this setting?

Thanks!