User blog comment:PsiCubed2/How to make Deedlit's Mahlo-level notation more intuitive/@comment-35470197-20180807000338/@comment-30754445-20180807141325

Suffice to say that I haven't understood 90% of what you've written there. :-)

Remember that the vast majority of the guys here (myself included) are not set theory experts. My own formal education in set theory ends with "Set Theroy 101" I've learned in college. Most of the other people here are even less well-versed in the topic than I am.

Of-course, that's not the impression you'll get from casually reading these forums, because:

(1) Many people here do know all kinds of bits and pieces of set theory that are relevant to googology. Many people here have a pretty good idea what ordinals are, or how fixed-points and Veblen functions work. But you gotta understand, that knowing how to "count" up to (say) Γ₀ is a completely different thing than truly grasping the underlying theory.

(2) Googologists tend to be impatient when it comes to "conquering" larger and large numbers (and ordinals), so they tend to jump the gun and start using advanced concepts way before they are ready for them.

(I, personally, try to resist this temptation. But as you've seen in the past few weeks, I'm not entirely immune to this craze either)

In short, what you gotta understand, is that most people here (myself included) don't even know what a Mahlo cardinal is exactly. Nor do we need to know. The Mahlos themselves aren't particularly interesting to a googologist. What we do need to know, is that M is big enough to provide the basis for a collapse function that enumerates the various kinds of inaccessibles.

Of-course, to actually invent such a function, one needs to be extremely well-versed in the topic. Especially if we also want to make sure that our invention is consistent (which isn't at all obvious, given that even the existence of Mahlos is undecidable in ZF/ZFC).

But thankfully, experts like Rathjen (and later Deedlit, who made Rathjen's ideas more accessible) already laid this groundwork for us. That's why my own efforts, at this moment in time, are geared towards mastering Deedlit's notation. TBH I'm not particularly interested in the Mahlos themselves. I'm only interested in how they collapse to countable ordinals.