User blog comment:P進大好きbot/Relation between an OCF and an Ordinal Notation/@comment-30754445-20180810102658/@comment-35470197-20180811213337

@PsiCubed2

> That's not a "tautology". It's an explanation of how the term "OCF" is used here.

Maybe you are considering language-theoretic tautology. I meant logical tautology. The explanation is of a type "(P wedge Q) -> P" in propogitional logic, which is a tautological statement.

> Can you give an example where the imprecise usage of the term "OCF" results in such a problem? If not, then it's just a semantic difference.

Problems occurs when googologists misunderstood the notion of a real (set thoertic) OCF as an ordinal notation containing such a symbol. They learn "Ok, imitating the expansion rules like those, I obtain a very strong OCF". When we point out that it lacks axiomatic explanation using set theory, then thay would say "it has nothing to do with set theory, and the strength is obvious because it has a similar expansion rule as another one".

If one drops one condition from the definition of an OCF, then the strength will become completely different, even if how it looks does not become so different. The point is that they could not understand "where to see" in order to observe the "similarity" respecting the strength.

> What I would mind, is if someone made a jumble of definitions and symbols, and declared he had created an OCF just because of some vague visual similarities.

Maybe this is the same as what I said above. If googologists see an OCF just by an aspect of an ordinal notation, then they would think that the strength of it is ensured by how they look but not by how they actually spread onto ordinals below greatly large ordinals without skipping. Such an argument is absolutely sensitive as you know, and how they look similar as notation systems does not ensure how they work well as OCFs.

Perhaps you may think that this problem is not derived from the confusion of the terminology, but I strongly think so.

> And while your notation may be computable (I'm not sure because I haven't understood everything you've written there), it suffers from a similar catch: Writing the explicit rules for it are practically impossible (even though it may be possible in principle).

Ok. I understand what you mean. Although it is actually possible (because I defined expansion rules in syntax theoretic way), it is impossible for human beings to compute. Only computers can, if they have sufficient memory. That is why I said that it is useless for analysis.

@Alemagno12

> Sources?

Although I have not checked it, the source is here.

http://web.mit.edu/dmytro/www/other/OrdinalNotation.htm#A8.2