User blog comment:Syst3ms/A formal definition for UNOCF/@comment-35470197-20180728080043/@comment-35470197-20180728123317

> Yes, \(\ddots\kappa \geq \kappa\), since you can't decrease an ordinal without FSes

Sorry, I mistook the question. I should ask whether \(\textrm{cof}(\ddots \kappa) \geq \kappa\) or not. If \(\textrm{cof}(\ddots \kappa) \geq \kappa\), then it conflicts the limit rule.

What is \(I\) in your definition? Do you define the OCF under \(\textrm{ZFC} + \textrm{Inaccessible}\) but not \(\textrm{ZFC}\)? Moreover, in the inaccessible rule, when \(\kappa = I\) and \(\alpha = I + I + I\), then the \((\beta,\delta)\) is not unique. Then \(\psi_{\kappa}(\alpha)\) is not well-defined.

And what is the answer of the following question?

> You state that there is no such an expression (and hence \(\psi\) is well-defined), right?

Namely, if an ordinal \(\alpha\) admits an expression of the form \(\ddots \kappa\), then the expression is unique, right?