Analyzing the Tiering System

[The_2nd_Existential_Seed]

... i feel personally High 1-A could work assuming the whole "conceptually beyond Outerversal Hierarchies" thing is what we use for it.

 

[Karter406]

Nice!

 

[Nepuko]

Yea no Apeiro pls. ''shivers''

 

[Sera_EX]

Treating this wiki as if it were an actual real-world job that you can "waste valuable time" on instead of an accuracy/fun-driven project that can take its time getting to the important point is why it's common for people to comment it is declining.

Considering the recent growth of "composite cosmology" verses, Seed's hypothetical isn't even a hypothetical. There are quite a few popular verses out there that deal with "obscure" mathematical hierarchies, so it's a worthwhile question.

I'm treating this as a job now? Jesus, all I said was we should use fictional examples instead of a thousand "what ifs", otherwise we'd end up derailing based on just that. I was wrong and Seed had an actual fictional example, Marvel, though we still shouldn't derail too mich on specific verse examples. This whole comment of yours was completely unnecessary as it hardly even addresses my argument and takes offense to something I never even said.

 

[The_2nd_Existential_Seed]

Just to note I was agreeing with Kepekley 2nd paragraph not neccessarily the 1st paragraph. I feel it's more like an attempt at organization and tidiness in this attempt than treating it as a job Kepekley. But you are significantly wiser at this type of thing so feel free to disregard my opinion.

 

[Antvasima]

I am probably the only person in this wiki who treats it like a real job, but that is a derailment from the main topic. Let's drop the subject please.

 

[Andytrenom]

I genuinely don't get why "apeiroverse" is used

"Verse" implies you are defining a certain type of multiverse and the character gets their rating via destroying/creating/controlling it. If instead of that you are defining qualities that a character can possess, then it really wouldn't fit

And tier 0 as far as I can see is still focused on the nature of a character, rather than the nature of a place. What would you even say the Apeiroverse is if asked? The character?

 

[Nepuko]

Better to keep it as "Boundless" imo.

 

[Antvasima]

I am personally fine with boundless.

 

[Maxnumb231]

Okay then. Thank you Sera for your time. Because based on the full context of the scan Marvel wasn't just referring to "Aleph".in describing the concept of trasnfinite .. He was talking about Cantor's entire theory of transfinite numbers and that it describes the Multiverse entire [ at least before they got into the higher-dimensions... They are talking about realities here]... Meaning transfinite in Marvel is equivalent to the highest thing in cantors theory involving numbers which I'm utterly confused on how to convert this properly.

Here is the scan but I'm certain people are well aware of it (https://comicvine1.cbsistatic.com/u...02593/3070536-drstrangesorcerersupre21-18.jpg)

Sure that statement can be legit and it mentioned but that is necessarily quantifiable feat and it doesnt translate to the tiering itself. And that statement is already wrong from aleph naught to aleph one is not cknsidered to be infinitely greater but weakly inacessible to aleph naught and this goes in for aleph one to aleph two. So that statement is already in its wronging.

 

[Maxnumb231]

Also to remind "infinite degrees of above outerversal" or what would be considered 1-B would if we say 1-A would be a different name then it woild just just be high degree of 1-B. If we decide to have high 1-B, it would need to have infinite layers composing each layer is seemingly unreachable unless specifics sre needed

 

[Udlmaster]

Perhaps, what about "Absolute Infinity" as proposed by Cantor himself, which he then related to God, which is apt for who will be in those positions, often the Supreme being/Deity. (All this in relation to the name of Tier 0)

We needn't have the NLF that the Old One had, "Muh Omnipotence Tier 0" but instead have the actual Absolute Infinity from Cantor, where he said This glorious line;

"The actual infinite was distinguished by three relations: first, as it is realized in the supreme perfection, in the completely independent, extraworldly existence, in Deo, where I call it absolute infinite or simply absolute; second to the extent that it is represented in the dependent, creatural world; third as it can be conceived in abstracto in thought as a mathematical magnitude, number or ordertype. In the latter two relations, where it obviously reveals itself as limited and capable for further proliferation and hence familiar to the finite, I call it Transfinitum and strongly contrast it with the absolute."

 

[DarkDragonMedeus]

I still like Sera's option 3 based on a combination of hers and DonTalk's input.

 

[Nepuko]

I still like Sera's option 3 based on a combination of hers and DonTalk's input.

I cri everytiem :'(

 

[Andytrenom]

@Udl I remember asking about absolute infinity and being told it won't actually be tier 0 in the new system

 

[Ultima_Reality]

Absolute Infinity doesn't exist, period. It's not even a mathematical concept whatsoever, and is overall extremely poorly defined, as it is assuming a full totality of all cardinals is even inherently defined and set in stone within a given model of Set Theory, in the first place, which is obviously not true, given we have to assert the existence of large cardinals through additional axioms. "Set of all Sets" is itself completely meaningless, and can actually fall under the definition of an Inaccessible Cardinal, even.

 

[Kepekley23]

@Udl

"Absolute Infinity" is a rather meaningless term that has no proper usage or definition, so I disagree.

 

[Antvasima]

We can probably drop the "absolute infinity" term then.

 

[Udlmaster]

I don't mean using it for the requirement of Tier 0, I believe people are Misunderstanding.

I was proposing it for the Name of Tier 0, as Boundless doesn't have any relation the anything before it and is just a generic slap on name.

Absolute Infinity as defined by Cantor is much closer to what we would assume a Typical Tier 0 character would be, and it has a thematic naming as things below it are defined by Cantor's theory, and Cantor thought the idea of Absolute Infinity was the highest among his own theory.

And I don't get what you mean by "Defined and set in stone within a given mode of set theory, in the first place, which obviously isn't true"

If all cardinals aren't set/defined that it sound like that it's a poor choice for a system that is set and defined, and if they are set/defined, as they should be as they are mathematical and therefore have a order, then it's not obvious then, as it's just untrue.

But again, it's not to have it be the requirement but merely the name, instead of Boundless or Apieroversal

 

[Hrdlifil]

Hello to you all,

I like the option 2, that is this:

"

• The current 1-B becomes Low 1-B
• The current High 1-B becomes 1-B
• High 1-B becomes the tier for up to uncountably infinite higher planes/dimensions/stuff
• Low 1-A becomes baseline Outerversal and up, with infinite hierarchies on this scale receiving a "+" modifier next to the rating
• 1-A and 0 are basically the same as Option 1

"

Now we need to pick a set theoretical universe where we do our normalization that is where our tiering happens. For that I propose ZFC+GCH+there exists an inaccessible cardinal

I really love the idea of tier 0 beeing an inaccessible cardinal as it is the largest possible thing in this universe so exactly what we want from tier 0. More over in this universe we don´t talk about proper classes and that is a good thing, since there strictly speaking need not be a single size of proper classes as there may not be a bijection between proper class of ordinals Ord and proper class of Surreal numbers No.

However I think that we don´t need to use wordly cardinals for 1-A. So I propose this:

Outerverse level (Low 1-A) = N2 and onwards (N3,...,N¤ë, N¤ë+1,....)

Outerverse level+ (Mid 1-A) = N¤ë1 and onwards (N¤ë1,...,N¤ë2,....,N¤ë¤ë,....,N¤ë¤ë¤ë,......)

whateververse level (1-A) = first aleph fixed point a = Na where cof(a) = ¤ë and onwards

0 = Inaccessible cardinal k = Nk with cof(k) = k therefore k-th fixed point

This is ideal in my opinion.

 

[Ultima_Reality]

Just leaving this response to the points which DontTalk made that I think need to be more immediately addressed, since I will be leaving for a bit right now. I will adress his other arguments later:

Our own universes dimensional axis' aren't necessarily infinite, neither are our timelines axis'. It makes in my opinion no sense to start demanding infinite axis from higher onwards.

I can understand wanting to sort out the entirely empty microscopic higher dimensions that some physics theories use, but what we should demand is large extra dimensions, not infinite extra dimensions

Yes. Hence why I already expressed that the new system is using R ^ n as a notation for when higher-dimensional spaces are either provably infinite or defined as infinitely larger than lower-dimensional stuffs by the verse it comes from. Higher-dimensional objects that are finite or have no context as to their nature are just considered some arbitrary subset or their respective coordinate systems.

This is purely an argument from semantics, really, as both of those things can lead to higher tiers anyways, and the new system accounts for both of them as well.

I have to disagree. There are euclidean Hilbert spaces of a dimensionality above any given cardinal number (note: any given. Not all at once!), which then have real valued coordinates.

One can certainly also define a few measures on them, though I don't know if any of those quantifies size in an intuitive fashion.

Do you have some examples backing this up? You certainly cannot embed or define some space with a cardinality/basis greater than the reals within an Euclidean Space, much less a Real Coordinate Space, which has cardinality equal to the real numbers and is pretty much just an Euclidean Space equipped with the notion of a dot product.

I wish to point out that classes can only contain sets. "Classes" that could actually contain everything that has a certain property are paradox!

I am referring to the concept of Small Classes, as defined in Von Neumann-Bernays-Gödel Set Theory, which are pretty much just prototypical sets: In it, all sets are types of Classes themselves.

Wait, now I'm confused. Why are you using classes if you are working with cardinals. For a start a non-set class has no cardinality regardless of its size.

And why does uncountable end at aleph one?!? All other cardinals are also uncountable?

Because at this point we are just defining classes of objects which exceed/are outside of arrangements of the real and complex numbers, assuming GCH holds in the first place. I should also note that Small Classes can in fact have cardinality, as they are (just slightly more specific) sets themselves, as I said above: Proper Classes are the ones that can't have cardinality and don't exist as sets, you seem to be mixing up the two notions here.

I literally never said this throughout my entire post. I said the set of Real Numbers ends at aleph-one under the assumptions made in the OP.

Inaccessible cardinals makes things way too complicated. I have honestly no idea which practical consequences you envision that has. Just state where 1-A starts by giving the concrete cardinal, or better yet describe what the cardinal means in terms of difference of scale.

E.g. If N are the natural numbers and P() denotes the powerset, one could use something like |{N, P(N), P(P(N)), P(P(P(N))),...}|. In words that would equate to transcending an infinite hierarchy. (Whether in terms of points, order, or by replacing each with a space with correspondingly many dimensions)

Though I personally would try to put it into simpler terms than actually pulling out cardinals. If that doesn't end up specific enough to use one can still consider explaining it in reference to cardinals.

I don't know why you keep insisting this stuff can't be possibly broken down into simpler parts, especially in relation to Inaccessible Cardinals, which are literally the entry point to the large cardinal hierarchy and the ones which don't really have to get into all of the more technical, nuanced aspects present in larger cardinal axioms. Assuming we are choosing the first option of what I proposed for this aspect, that is, since there is a person who thinks otherwise, as you can see above.

 

[Matthew_Schroeder]

The real big problem with these type of threads is that they invariably attract the kind of people who think that just slapping big words together will make them sound smarter than they really are.

 

[Sera_EX]

Let me rephrase that for you:

The real big problem with these type of threads is that they invariably attract the kind of people who think that just slapping big words together will make characters seem stronger than they really are.

 

[Andytrenom]

Let's avoid vague remarks insulting unspecified groups of peoples please. They are unnecessary and easily start conflict

 

[DarkLK]

I think the option 2 looks better than others. I'm not sure that there needs a separate tier for infinite levels of outerversal should have a separate tier.

 

[Sera_EX]

Let's avoid vague remarks insulting unspecified groups of peoples please. They are unnecessary and easily start conflict

That's not an insult, and there's a reason I rephrased his reply to be more on point with the topic at hand.

 

[Andytrenom]

His comment very much has an attitude of putting down people unnecessarily. Whether you classify that as an insult doesn't really matter, it's not productive at all

 

[Antvasima]

I think that Andy referred to Matthew's comment, in which case I agree that it was unnecessary.

 

[Antvasima]

@DarkLK

I would personally much prefer to keep different types of hierarchies distinctive from each other, so I prefer option 3.

 

[DarkLK]

@Antvasima

Both the beginning (baseline) and the peak are within the same hierarchy, so I do not think that endless levels (peak) should be singled out separately.

 

[Sera_EX]

His comment very much has an attitude of putting down people unnecessarily. Whether you classify that as an insult doesn't really matter, it's not productive at all

I was talking about my comment. I rephrased what he said because how he worded it was indeed unnecesary.

 

[Apex_Predator_GX]

So basically a character must be Higher Dimensional and be Infinite in size to be considered for tier High 3-A and above?

 

[Antvasima]

@DarkLK

Please elaborate.

 

[Sera_EX]

He's saying baseline 1-A and peak 1-A are part of the same outversal hierachy. Just beginning and end.

 

[Antvasima]

Okay. I do think that an endless hierarchy of 1-A levels should constitute a separate tier though. It helps us distinguish Featherine and Yog-Sothoth from the Choushin and regular baseline Outer Gods for example.

 

[DontTalkDT]

To shorten this

Yes. Hence why I already expressed that the new system is using R ^ n as a notation for when higher-dimensional spaces are either provably infinite or defined as infinitely larger than lower-dimensional stuffs by the verse it comes from. Higher-dimensional objects that are finite or have no context as to their nature are just considered some arbitrary subset or their respective coordinate systems.

This is purely an argument from semantics, really, as both of those things can lead to higher tiers anyways, and the new system accounts for both of them as well.

I don't know why the notation matters to the subject (though I already said that noting them as R^n isn't the best idea, as our spacetime is not that by any means)

And as I said, I'm against infinite being demanded, as even for our real life universe it doesn't have to apply. It isn't an arbitrary subset of some larger space of same dimension and if it were it wouldn't matter at all.

I don't know why you keep insisting this stuff can't be possibly broken down into simpler parts, especially in relation to Inaccessible Cardinals, which are literally the entry point to the large cardinal hierarchy and the ones which don't really have to get into all of the more technical, nuanced aspects present in larger cardinal axioms. Assuming we are choosing the first option of what I proposed for this aspect, that is, since there is a person who thinks otherwise, as you can see above.

You can't even proof that inaccessible cardinals exist.

Mathematics that are not even well supported by ZFC (it's consistent with ZFC, but you know what I mean) is neither easy, nor intutive, nor can I imagine why in the world you want to do absolutely anything with it in regards to our tiering.

I can honestly not imagine that we have a single fiction on this side that actually has a feat that would qualify for this, unless maybe we have some fiction that mentions it verbatim or the fiction just does "lol, transcend mathematics/cardrinals".

And honestly, worldly cardinals aren't any better.

In any case, if we have to do some explicit 1-A tiering, I would go for Sera's idea of setting the borders at infinite levels of existence above basic outerversal and/or above that. And that is just really not well represented with any of that.

In fact, IMO there is no need to represent them that mathematically at all. All we might need to do is give a bit more of a clearer quantification for what does or does not constitute a higher level.

 

[Karter406]

If a being is stated to be a higher-dimensional super-omnipotent god thing, but it's beaten by a bunch of children good at fistfighting, should it be placed at a lower tier than the higher-dimensional super-omnipotent god beings who won in the end? Or should "Lost to literal children" be placed in its page as an anti-feat?

 

[LuciusIsMas]

Wait but what if a verse only has 3 dimensions but the character is beyond all 3 dimensions and beyond existence/non existence blah blah in a verse with only 3 dimensions.

 

[DarkLK]

Okay. I do think that an endless hierarchy of 1-A levels should constitute a separate tier though. It helps us distinguish Featherine and Yog-Sothoth from the Choushin and regular baseline Outer Gods for example.

I don't quite understand how this relates to them. They are above such ladders, where each step is equal to such a hierarchy.

 

[ÆONS]

Jesus, so many big words, mathematical notations, semantics, bibles, superficial comments, and the likes being thrown around here. In any case, I am inclined to agree with option 3. I don't see much of a reason to change or merge the other tiers with one another since they are already well defined (besides the business about countably and uncountably infinite-dimensional stuff), the only real main issue is with the 1-A/0 business.