User blog comment:Hyp cos/Attempt of OCF up to Stability/@comment-35470197-20181026043805

Are \(\alpha\) and \(\beta\) in the definition of the notion of a reflection instance ordinals?

Is \(\varpi\) in the suffix of \(\varphi\) an ordinal which is not necessarily an uncountable regular cardinal?

What is the well-founded order on the class of reflection instance, which is necessary to define \(\psi_{\varpi}\) through transfinite induction?

Also, do you have an ordinal notation system associated to \(\varphi\)'s?