User blog comment:Syst3ms/YAUD/@comment-30754445-20180810132619/@comment-30754445-20180813162938

According to the strict definition, an OCF is nothing more than a function that can convert any ordinal into "an ordinal smaller than X" (for some X).

And when we talk about "OCF-base systems", we are refering to actual ordinal notations that use one or more functions like the above. Note that we don't need to list all the functions explicitly. Usually they are defined all at once, by giving a general rule for how the a-th function collapses the ordinal b.