Can we write this a bit differently? I think this formulation could be misinterpreted as us saying that any 4-dimensional space is the R^4 in some sense.
IMO we need a definition of "causally closed/isolated" on the page (or replace the terms with something more self-expanatory). This could for example be misinterpreted as being outside each others cosmological horizons.
To Low 1-A: "most specifically ones comparable to the set of all real numbers in size" I think it makes more sense to say amount than size here, as what the size of the set of real numbers is is easy to misunderstand. Maybe something like ". More specifically ones for which the amount of dimensions, layers or levels is equal to the amount of real numbers."
Noted.
If we use cardinals on the main page (as opposed to for example just using them in the mathematical explanation part of the Dimensional Tiering page) the page needs to include a simple explanation for what they are and mean. The average users will otherwise get confused by a sentence like above. I would in that regard rather have a short handwritten explanation tailored to out purposes than simply wikipedias.
The page itself will contain a link to a more in-depth article which elaborates on the clockwork beneath the hood of the system, probably followed by some brief explanations + links to videos that concisely explain the concepts used here.
So, yeah, no worries.
To High 1-A & 0: Personally I'm still against using cardinals we don't even know to exist as definition for this.
Large Cardinals don't normally exist within a given set-theoretical Universe, but they can be added as additional axioms which extend its scope, just like one doesn't even have to consider the axiom of infinity as part of a certain framework, but is still free to do so anyways. The fact that they exist more as additional axioms and postulates than inherent parts of a given Universe also fits with the whole definition of High 1-A, as in, transcending and being fully external to Outerversal Hierarchies in general.
Is transcending an infinite outerversal reality-fiction hierarchy High 1-A?
Yeah, so long as they are actually external to it, as opposed to being transcendent in the sense of being "at the top", but still part of the overall hierarchy, if you get what I mean. It's not actually any different from the way High 1-B and 1-A interact, really, it's just on a larger scale.
If a character is intended to be above any kind of hierarchy is that High 1-A or 0 or is such a statement irrelevant due to the entirely different sizes and nature of hierarchies in different fictions?
"Transcending any kind of hierarchy" is such a vague statement that it should probably be analyzed more thoroughly based on whatever context there is to it. If it is in relation to 1-A Hierarchies, then that seems to be a fairly straightforward example of High 1-A.