User blog comment:Syst3ms/A sketch for an — actually — formal definition of UNOCF/@comment-35470197-20180803231131/@comment-30754445-20180811193450

"The idea of well-defining UNOCF as an actual OCF has been pretty much been dropped. It's now being well-defined as an ordinal notation instead (see here). So now it can have any strength we want it to have (as long as we define things correctly), and therefore be able to go beyond Deedlit's weakly compact OCF."

That's quite wrong.

It doesn't matter if UNOCF is an actual OCF or not.

What matters is the strength of the concepts used, and these concepts have to come from somewhere. Either you borrow them from someone else, or you develop them yourself.

If you borrow them from somewhere, then you are limited by the strength of what you borrowed.

If you develop them yourself, you're limited by your knowledge and experience. And unless you are very well-versed in the intricate details of set theory, this will not allow you to go much further than the concepts you borrowed. Remember the "secret ingredients" analogy I've given in my previous post. This metaphor doesn't depend on UNOCF being an OCF.

It looks like your argument is something like this:

"We've tried to do it as a proper OCF, but all the pesky details kept turning out wrong, so f**k set theory. We'll do things our own way, and things will run more smoothly"

But it doesn't work that way. By dropping the usual set-theoretic concept like Mahlos and Weakly-Compact Cardinals, you are depriving yourself of very power tools. You can't just pop the symbols I,M,K,T from a hat and expect it to result in a powerful system.

Or do you actually think that you (any of you) can re-invent the wheel, and create tools of similar power without using set theory? I'm sorry, but that's just silly.

As for your analysis:

Even if we'll assume, for a moment, that it is true, it still doesn't addressed my main objection: You can't go much beyond standard K, because you don't have any existing example of what a post-K (a pi-4 reflecting) notation looks like.

How do you plan to continue such an analysis, when you have no yardstick to compare it with? Just because it seems "much larger than Deedlit's K" doesn't mean anything.