User blog comment:Syst3ms/A sketch for an — actually — formal definition of UNOCF/@comment-35470197-20180803231131/@comment-35470197-20180808112018

> Ask P Bot, but I'm pretty sure ordinal notation and OCF are not the same.

"Ordinal Notation" = a shorthand of "Ordinal Notation System" = an arithmetic system of formal strings consisting of enumerable family of alphabets equipped with an well-order

"OCF" = a shorthand of "Ordinal Collapsing Function" = a roughly used terminology of a set theoretic system of functions defined on a class of ordinal numbers which collapse (the size, the cofinality, or another degree of) cardinals

Although this terminology is used in mathematical papers in the way above, googologists here often call an ordinal notation an OCF. Therefore this terminology is a little ambiguous here.

Usually we strongly need an OCF in order to ensure that a given ordinal notation actually works in a desired way, but I sometimes construct ordinal notations without OCFs but with the PTO of ZFC :P