User blog comment:Hyp cos/Attempt of OCF up to Stability/@comment-35470197-20181026043805/@comment-11227630-20181026045142

Lower case Greek letters (except\(\psi\)) always denote ordinals. All of them, including the subscripted \(\pi\), are not necessary to be admissible, also not uncountable. They may have some reflecting property if they are in some set \(A_\pi\mathbb X\).

Reflection instances, in this definition, are not sets or ordinals, but just "character strings".

And what do you mean by "an ordinal notation system associated to \(\varphi\)'s"?