User blog comment:Ecl1psed276/BM2 Analysis - A Summary/@comment-30754445-20180709051740/@comment-35470197-20180713110632

@Alemagno12

> First, what are you referring to with ordinal notation and ordinal function?

I referred with "ordinal notation" (resp. "ordinal function") to a function from a countable set (resp. a class) to the class \(\textrm{ON}\) ordinals. The reason why I used these terms is because some googologists refer with "OCF" to both of them in a single context with ambiguity. So I just wanted to avoid the ambiguity in my statements.

> And second, you don't need inaccessibles to define an OCF as strong as other standard inaccessible OCFs - in fact, you can just use nonrecursive ordinals and get the same results.

What do you mean by saying "standard" here?

Maybe you are refering with "the same results" to ordinal notations with the same strength, as Rathjen's OCF was replaced by his recursive analogue in order to verify the well-foundedness of the primitive recursive interpretation under ZFC (without inaccessibles). I could not understand what you wanted to say. Is that relevant to what I mentioned?