Insufficient Explanations on the Vs. Battles Tiering Pages (STAFF ONLY)

[KingPin0422]

Sorry, I modified the description again because some parts of it were bothering me. I hope that's fine.

On that note, are any changes to my given tier 0 description needed?

 

[Antvasima]

I am not good at advanced mathematics anymore. My apologies.

Let's wait to see what the others say.

 

[The_Impress]

I'll try contacting Ultima offsite ig

 

[Antvasima]

Thank you. I would greatly appreciate if he tries to become more active in extremely important revisions in which we genuinely need his help.

 

[Ultima_Reality]

What do you think

I'm largely fine with KingPin's suggestions, yeah. Given both DontTalk and I agreed to postpone our above discussion for later, I don't exactly have much to say beyond that.

 

[Ultima_Reality]

There you are Ultima!

Do wish I wasn't.

 

[The_Impress]

so I believe we need @DontTalkDT's input and then Derp's suggestion's golden?

 

[Ultima_Reality]

Pretty much.

 

[Antvasima]

I'm largely fine with KingPin's suggestions, yeah. Given both DontTalk and I agreed to postpone our above discussion for later, I don't exactly have much to say beyond that.

Thank you for helping out.

If @DontTalkDT also gives his final verdict, I think that we can apply what was decided here.

 

[DontTalkDT]

Alright, here's a (hopefully) finalized version of the new High 1-A description, using DontTalk's suggestion as a reference point:



I feel that "Even the amount of cardinals between such a cardinal and aleph-2 (which defines 1-A) is larger than many (typically all) regular cardinals." is unnecessary to include in the description because it's completely redundant. As in, "the amount of cardinals between [an inaccessible cardinal] and aleph-2" is... an inaccessible cardinal. Saying that it's "larger than many/all regular cardinals" wouldn't really be appropriate, either, given that an inaccessible cardinal is itself a regular cardinal. In fact, under ZFC, every finite-index aleph number is a regular cardinal, but every infinite-index aleph number is instead singular. The first regular cardinal you can encounter after the finite-index alephs is an inaccessible cardinal, which is unprovable within ZFC without adding another axiom to permit discussion of inaccessible cardinals. Therefore, in a certain sense, even 1-A+ is larger than all regular cardinals (in ZFC), and so the aforementioned detail is superfluous, in my opinion.

A bit of an unlucky formulation on my part there. When I said regular cardinal there, I didn't mean regular in a mathematical sense. I meant regular as in ZFC non-large / accessible cardinal. Replace the word regular with "accessible" maybe. Like:

Even just the amount of cardinals between such a cardinal and aleph-2, which defines 1-A, is larger than many (typically all) accessible cardinals, including aleph-2, aleph-3, aleph-4 etc.

The point of that part was to make clear that even the amount of levels of infinity we are talking about themselves are of a massively uncountable degree. You know, to make the quantitative difference between the levels more graspable for those with some understanding of how ZFC cardinals work.

 

[Antvasima]

@KingPin0422

 

[KingPin0422]

A bit of an unlucky formulation on my part there. When I said regular cardinal there, I didn't mean regular in a mathematical sense. I meant regular as in ZFC non-large / accessible cardinal. Replace the word regular with "accessible" maybe. Like:

The point of that part was to make clear that even the amount of levels of infinity we are talking about themselves are of a massively uncountable degree. You know, to make the quantitative difference between the levels more graspable for those with some understanding of how ZFC cardinals work.

Oh, okay. I see what you mean. Tell me how this looks, then:

High 1-A | High Outerverse level: Characters who can affect objects that are larger than what the logical framework defining 1-A and below can allow, and as such exceed any possible number of levels contained in the previous tiers, including an infinite number. Practically speaking, this would be something completely unreachable to any 1-A hierarchies; even an infinite number of these hierarchies, each with infinite levels of infinity and with the lowest level of each hierarchy being infinitely bigger than the entire previous hierarchy, wouldn't approach this tier.

A concrete mathematical representation of this tier is an inaccessible cardinal, which in simple terms is a number so large that it cannot be reached ("accessed") by smaller numbers, and as such has to be "assumed" to exist in order to be made sense of or defined in a formal context (Unlike the standard aleph numbers, which can be straightforwardly put together using the building blocks of set theory). Even just the amount of infinite cardinals between the first inaccessible cardinal and aleph-2 (Which defines 1-A) is greater than any aleph number, such as aleph-0, aleph-1, aleph-2, etc. More information on the concept is available on this page.

Also, I think we should adjust the description for tier 0 to match current standards, as well as to illustrate the gap between baseline High 1-A and baseline 0. Maybe just add a paragraph looking something like this (with the blanks filled in, of course):

Mathematically, the lowest level of this tier can be represented by a Mahlo cardinal, which in simple terms is [insert easy to understand explanation here]. The gap between inaccessible cardinals and Mahlo cardinals is far greater than the gap between standard infinite numbers and inaccessible cardinals: [insert another explanation here]. After Mahlo cardinals comes a vast hierarchy of even greater large cardinals: refer to this Wikipedia article for more information.

 

[DontTalkDT]

Oh, okay. I see what you mean. Tell me how this looks, then:



Also, I think we should adjust the description for tier 0 to match current standards, as well as to illustrate the gap between baseline High 1-A and baseline 0. Maybe just add a paragraph looking something like this (with the blanks filled in, of course):

I'm not sure that you can say that they are bigger than any aleph numbers actually. Do you have some proof of that?

Edit: Actually, thinking about it "accessible" cardinals would obviously not work as well, as the successor cardinals of them would be accessible. Would "Not Large Cardinals" or "Not Inaccessible Cardinals" work? I'm not sure. One can't proof that Large/Inaccessible cardinals are larger than any cardinal that might be in ZFC after all.

What the tier 0 stuff is concerned... when have we settled on the mahlo cardinal and why?

 

[Antvasima]

I'm not sure that you can say that they are bigger than any aleph numbers actually. Do you have some proof of that?

Edit: Actually, thinking about it "accessible" cardinals would obviously not work as well, as the successor cardinals of them would be accessible. Would "Not Large Cardinals" or "Not Inaccessible Cardinals" work? I'm not sure. One can't proof that Large/Inaccessible cardinals are larger than any cardinal that might be in ZFC after all.

What the tier 0 stuff is concerned... when have we settled on the mahlo cardinal and why?

@KingPin0422 @Ultima_Reality

 

[KingPin0422]

I'm not sure that you can say that they are bigger than any aleph numbers actually. Do you have some proof of that?

Well, technically, inaccessible cardinals can be written as aleph-k for some inaccessible cardinal k, and the same holds for... pretty much any large cardinal property, really. The issue is that large cardinals, by their general definition, are literally "too big" for ZFC (why do you think they're called large cardinals?), and while the consistency strength of large cardinal axioms =/= the size of the large cardinals that observe them (huge cardinals seem to be smaller than supercompact cardinals, for instance, despite the existence of a huge cardinal being a "stronger statement" than the existence of a supercompact cardinal.) Simply put, the large cardinal hierarchy is kind of just nonlinear.

Anyway, I don't have like, a mathematical proof behind what I just said. It just seemed intuitive to me, but I remembered that large cardinals can be expressed in terms of aleph numbers - it's just that most avoid doing that because it's not useful.

Edit: Actually, thinking about it "accessible" cardinals would obviously not work as well, as the successor cardinals of them would be accessible. Would "Not Large Cardinals" or "Not Inaccessible Cardinals" work? I'm not sure. One can't proof that Large/Inaccessible cardinals are larger than any cardinal that might be in ZFC after all.

Now, I do wanna ask: from where do you get your claim that inaccessible cardinals can't be proven to be larger than anything in ZFC? An inaccessible cardinal, at least for our purposes, is a cardinal number k with the following properties:

• Uncountable: k is larger than aleph-0.
• Regular: k cannot be reached by the union of less than k sets which are all smaller than k.
• Strong limit: k cannot be reached by repeated power set operations.

Given all of this, I'm not sure I understand how something comparable to inaccessible cardinals in size can be proven by ZFC without any additional axioms.

What the tier 0 stuff is concerned... when have we settled on the mahlo cardinal and why?

Well, you asked this earlier:

As for a mathematical presentation of Tier 0: Why not just say it's infinite cardinals greater than whatever cardinal is High 1-A? Isn't transcending an infinite hierarchy above High 1-A how non-mathematical characters typically reach Tier 0?

And since the next large cardinal property after the inaccessible cardinal property (which is currently the basis for High 1-A) is the Mahlo cardinal property, I naturally assumed that that's what you wanted. On the other hand, the system currently doesn't seem to accommodate worldly cardinals, which was an issue I used to have back when the tiering revisions were first being carried out, but I don't know if they're like, relevant enough to be included? What do you think?

 

[Antvasima]

Thank you very much for helping out.

 

[DontTalkDT]

Well, technically, inaccessible cardinals can be written as aleph-k for some inaccessible cardinal k, and the same holds for... pretty much any large cardinal property, really. The issue is that large cardinals, by their general definition, are literally "too big" for ZFC (why do you think they're called large cardinals?), and while the consistency strength of large cardinal axioms =/= the size of the large cardinals that observe them (huge cardinals seem to be smaller than supercompact cardinals, for instance, despite the existence of a huge cardinal being a "stronger statement" than the existence of a supercompact cardinal.) Simply put, the large cardinal hierarchy is kind of just nonlinear.

Anyway, I don't have like, a mathematical proof behind what I just said. It just seemed intuitive to me, but I remembered that large cardinals can be expressed in terms of aleph numbers - it's just that most avoid doing that because it's not useful.

Now, I do wanna ask: from where do you get your claim that inaccessible cardinals can't be proven to be larger than anything in ZFC? An inaccessible cardinal, at least for our purposes, is a cardinal number k with the following properties:

• Uncountable: k is larger than aleph-0.
• Regular: k cannot be reached by the union of less than k sets which are all smaller than k.
• Strong limit: k cannot be reached by repeated power set operations.

Given all of this, I'm not sure I understand how something comparable to inaccessible cardinals in size can be proven by ZFC without any additional axioms.

I mean, for a start I have been unable to find a statement that says that they actually are actually larger. So obviously I have an interest in checking it's actually true.

However, if you wish to hear my intuition on the matter: I believe for an inaccessible cardinal k the statement "k is larger than any cardinal that may exist according to ZFC" is one that must be either wrong or undecidable. The reason for that is that the statement "k exists" is undecidable within ZFC. That means that k in and of itself could be a cardinal that exists according to ZFC, but we can't prove it. It's important to remember that in an axiomatic system like ZFC a statement can be true yet unprovable.

However, the statement "k is larger than any cardinal that may exist according to ZFC" can obviously only be true, if k in itself does not exist within ZFC. Otherwise, you would prove k > k, which is a contradiction. Therefore proving "k is larger than any cardinal that may exist according to ZFC" would as consequence prove "k does not exist according to ZFC".

However, that is problematic. Within ZFC alone it immediately gets a contradiction: "k exists" isn't decidable yet you just decided it.

One could now argue that instead of ZFC one should look into the axiom system of 'ZFC + k exists'. In that system "k exists" is decidable so the first contradiction doesn't occur. But it gives rise to a new problem: If you in 'ZFC + k exists' prove "k does not exist according to ZFC" then you also prove "k does not exist according to 'ZFC + k exists'". Reason for that is that just adding an axiom can make undecidable statements decidable, but not make a false statement true (or vice versa). If reasoning from 10 assumptions indicates something is false, than adding an 11th assumption (that can just go completely unused) won't change that it is false. As such you reach a contradiction again, as you would have shown that "k exists" per axiom and "k doesn't exist" per theorem.

Well, maybe I make a mistake somewhere there, set theory and formal logic aren't my area of mathematics, but point is that we probably shouldn't make the claim without having solid proof.

Well, you asked this earlier:

And since the next large cardinal property after the inaccessible cardinal property (which is currently the basis for High 1-A) is the Mahlo cardinal property, I naturally assumed that that's what you wanted. On the other hand, the system currently doesn't seem to accommodate worldly cardinals, which was an issue I used to have back when the tiering revisions were first being carried out, but I don't know if they're like, relevant enough to be included? What do you think?

When I said that what I had in mind was the taking infinite successor cardinals. Part of that suggestion was to use aleph-omega for 1-A so my suggestion for tier 0 was basically just infinite successors after aleph-omega. (Is it aleph-2*omega or aleph-omega^2? I'm not too good with ordinal arithmetic.)

What do you mean with Mahlo cardinals are the next large cardinal? Can't one construct large cardinals of virtually any size if one just chooses the right axioms?

 

[Antvasima]

Thank you very much for helping out to you as well. You are awesome.

 

[Ultima_Reality]

I mean, for a start I have been unable to find a statement that says that they actually are actually larger. So obviously I have an interest in checking it's actually true.

Because it's not really true to begin with, by the way. An "aleph" is at the core just the cardinality of a set that is both infinite and well-ordered (Cardinals are a type of ordinal, after all), and since the Axiom of Choice determines that any set is well-orderable, then there is no infinite cardinal without an aleph number. You can have one if you ditch Choice, but by then you already let go of a thing that keeps most of standard mathematics in place, anyway.

Overall, I think we shouldn't concern ourselves too much over those specifics and get straight to the point, largely. So just elaborating on how High 1-A is something that cannot be reached from below should suffice here, which means removing this part: "Even just the amount of infinite cardinals between the first inaccessible cardinal and aleph-2 (Which defines 1-A) is greater than any aleph number, such as aleph-0, aleph-1, aleph-2, etc. More information on the concept is available on this page." and keeping the rest.

 

[Antvasima]

Thank you for helping out, Ultima.

 

[DontTalkDT]

Because it's not really true to begin with, by the way. An "aleph" is at the core just the cardinality of a set that is both infinite and well-ordered (Cardinals are a type of ordinal, after all), and since the Axiom of Choice determines that any set is well-orderable, then there is no infinite cardinal without an aleph number. You can have one if you ditch Choice, but by then you already let go of a thing that keeps most of standard mathematics in place, anyway.

Overall, I think we shouldn't concern ourselves too much over those specifics and get straight to the point, largely. So just elaborating on how High 1-A is something that cannot be reached from below should suffice here, which means removing this part: "Even just the amount of infinite cardinals between the first inaccessible cardinal and aleph-2 (Which defines 1-A) is greater than any aleph number, such as aleph-0, aleph-1, aleph-2, etc. More information on the concept is available on this page." and keeping the rest.

Yeah, we actually figured out the fact that it isn't beyond all alephs already. What we were talking about is if one could fix the passage you quote by instead saying "Even just the amount of infinite cardinals between the first inaccessible cardinal and aleph-2 (Which defines 1-A) is greater than any non-large cardinal, such as aleph-0, aleph-1, aleph-2, etc."

It's also just a generally interesting question in regards to understanding our system in proper context, whether large/inaccessible cardinals are something like "larger than ZFC"/"larger than standard mathematics" or if they are just an intermediate stopping point within the whole standard ZFC hierarchy of cardinals.

 

[Ultima_Reality]

Yeah, we actually figured out the fact that it isn't beyond all alephs already. What we were talking about is if one could fix the passage you quote by instead saying "Even just the amount of infinite cardinals between the first inaccessible cardinal and aleph-2 (Which defines 1-A) is greater than any non-large cardinal, such as aleph-0, aleph-1, aleph-2, etc."

See, I'm warry of putting that description in there largely because even the notion of what a "large cardinal" is is extremely ill-defined, and I really don't want to force casual readers to go by such nebulous terms, especially since the purpose of the Tiering System page is to first give them a primer of it all that is then complemented by other explanation pages.

It's also just a generally interesting question in regards to understanding our system in proper context, whether large/inaccessible cardinals are something like "larger than ZFC" or if they are just an intermediate stopping point within the whole standard ZFC hierarchy of cardinals.

This is dipping its toes into Set-Theoretic Universalism vs Potentialism (That is, the question of whether the Universe of Sets is a single, completed collection that we "discover" larger parts of over time, or something that is constantly expanding as we posit stronger and stronger axioms), which is a whole philosophical conundrum that I'd rather not bring into the table. But if you pointed a gun to my head and forced me to give an answer, then I'd say we could treat it as the former, yeah.

For instance, take into account ZFC-Infinity: If we were to do analysis in such a framework, then it would be coherent to treat finite numbers as being the ordinals of that universe, and sets like N and R as being its proper classes, in the same way V, Ord and ON are to standard ZFC. Treating those as sets that could be played around with like any other would be something that the syntax of that theory would not be strong enough to support. Therefore, from a practical perspective it would be fair to say they are nonexistent objects with respect to that universe.

Large cardinals are much the same; take Hausdorff's original proposal of a weakly inaccesible cardinal, for instance: A cardinal that is both regular (Has a cofinality equal to its cardinality) and weak limit (Neither 0 nor a successor ordinal). Obviously, we couldn't really construct a number like that, nor exemplify it anywhere in the same ways we could do with "normal" ones: aleph-1 is regular, yes, but it is a successor cardinal; aleph-omega is a limit cardinal, but it is singular; aleph-omega+1 is regular, but it is a successor cardinal; aleph-omega+omega is limit, but it is singular again, and so on and so forth. And it comes to a point where all we can do is say "For the sake of argument, assume such a number exists."

 

[DontTalkDT]

See, I'm warry of putting that description in there largely because even the notion of what a "large cardinal" is is extremely ill-defined, and I really don't want to force casual readers to go by such nebulous terms, especially since the purpose of the Tiering System page is to first give them a primer of it all that is then complemented by other explanation pages.

Well, in that case what if we just put it as "Even just the amount of infinite cardinals between the first inaccessible cardinal and aleph-2 (Which defines 1-A) is greater than cardinals such as aleph-0, aleph-1, aleph-2, aleph-3,... or even many alephs which's index in itself is an infinite cardinal."

This is dipping its toes into Set-Theoretic Universalism vs Potentialism (That is, the question of whether the Universe of Sets is a single, completed collection that we "discover" larger parts of over time, or something that is constantly expanding as we posit stronger and stronger axioms), which is a whole philosophical conundrum that I'd rather not bring into the table. But if you pointed a gun to my head and forced me to give an answer, then I'd say we could treat it as the former, yeah.

No? This is a strictly mathematical question. No subjectivity or philosophy in it. It's the kind of stuff one could (potentially, if it's decidable) write mathematical proof about.

We are talking about two specific axiom systems. ZFC and ZFC+inaccessible cardinals exist. Within the latter (as it's obviously undecidable in the former) we want to know the truth value of the mathematical statement "Does ZFC imply the existence of a set S, with the property that |S| > k for some inaccessible cardinal k" or the (in our context) stronger statement "All sets S with the property 'ZFC does not imply S doesn't exist' and all inaccessible cardinals k have the property |S| < k". (The latter just being the mathematical formulation of whether ZFC may allow for larger than inaccessible cardinals on its own)

 

[Antvasima]

@Ultima_Reality @KingPin0422

 

[Ultima_Reality]

Well, in that case what if we just put it as "Even just the amount of infinite cardinals between the first inaccessible cardinal and aleph-2 (Which defines 1-A) is greater than cardinals such as aleph-0, aleph-1, aleph-2, aleph-3,... or even many alephs which's index in itself is an infinite cardinal."

Yeah, looks alright to me. Given we've already explained what aleph fixed-points are in the Tiering System Explanation Page, we can link that section of it too, so people aren't confused by the bolded tidbit (EDIT: Yeah, I misread that part. Although, nevertheless, alluding to fixed points probably doesn't hurt if we want to illustrate the size of those things)

Given all of this, I take it that we can already apply those descriptions to the system page? The other aspect of this discussion largely revolves around technical details that aren't really going to make it into the Tiering System page in any explicit form (For now, at least), so, might as well.

We are talking about two specific axiom systems. ZFC and ZFC+inaccessible cardinals exist. Within the latter (as it's obviously undecidable in the former) we want to know the truth value of the mathematical statement "Does ZFC imply the existence of a set S, with the property that |S| > k for some inaccessible cardinal k" or the (in our context) stronger statement "All sets S with the property 'ZFC does not imply S doesn't exist' and all inaccessible cardinals k have the property |S| < k". (The latter just being the mathematical formulation of whether ZFC may allow for larger than inaccessible cardinals on its own)

Apologies my misunderstanding, then. Although that doesn't really change my point much, as far as I can see. We can still compare two axiomatic systems: ZFC + "There are no Inaccessible cardinals" and ZFC + "There exists an inaccessible cardinal," and in the context of the latter model, the least inaccessible is larger than any cardinal whose existence is demonstrable in the former, just like ω is a proper class in ZFC-Infinity, and not a provable set. There is still a cut-off occuring between the two universes, which is more or less what the Generic-Multiverse view that Woodin proposes is all about (In this case, if you call the original universe of sets M, then you could refer to the two aforementioned models as N and N*, which in this case would be separate extensions of it realizing two statements that are consistent with its language)

(Granted, we run into issues with the Ω-Conjecture if we chose to take that route, which as far as I am aware is an unresolved issue, so, I suppose you might be warry of adopting that whole deal as a frame of reference)

 

[Antvasima]

Thank you for helping out, Ultima.

Would one of you be willing to write a draft for what should be added to our tiering system page then?

 

[Antvasima]

@DontTalkDT

 

[Ultima_Reality]

Would one of you be willing to write a draft for what should be added to our tiering system page then?

Something like this, I believe:

Low 1-A | Low Outerverse level: Characters who can affect objects with a number of dimensions greater than the set of natural numbers, meaning in simple terms that the number of dimensions is aleph-1 (An uncountably infinite number, assumed to be the cardinality of the real numbers themselves), and therefore that such objects fully exceed High 1-B structures, which have only a countably infinite number of dimensions. More information on the concept is available on this page.

Note that, if the High 1-B structure in question is a hierarchy of levels of existence, then simply being at the top of such a hierarchy does not qualify a character for this tier without more context, and an additional layer added on top of the "infinity-th" level of this hierarchy is likewise not enough. To qualify, they need to surpass the hierarchy as a whole, and not simply be on another level within it.

1-A | Outerverse level: Characters who can affect objects with a number of dimensions equal to the cardinal aleph-2, which in practical terms also equals a level that completely exceeds Low 1-A structures to the same degree that they exceed High 1-B and below. This can be extrapolated to larger cardinal numbers as well, such as aleph-3, aleph-4, and so on, and works in much the same way as 1-C and 1-B in that regard. Characters who stand an infinite number of steps above baseline 1-A are to have a + modifier in their Attack Potency section (Outerverse level+).

High 1-A | High Outerverse level: Characters who can affect objects that are larger than what the logical framework defining 1-A and below can allow, and as such exceed any possible number of levels contained in the previous tiers, including an infinite or uncountably infinite number. Practically speaking, this would be something completely unreachable to any 1-A hierarchies.

A concrete example of such an object would be an inaccessible cardinal, which in simple terms is a number so large that it cannot be reached ("accessed") by smaller numbers, and as such has to be "assumed" to exist in order to be made sense of or defined in a formal context (Unlike the standard aleph numbers, which can be straightforwardly put together using the building blocks of set theory). Even just the amount of infinite cardinals between the first inaccessible cardinal and aleph-2 (Which defines 1-A) is greater than cardinals such as aleph-0, aleph-1, aleph-2, aleph-3,... or even many alephs whose index in itself is an infinite number of cardinals. More information on the concept is available on this page.

0 | Boundless: Characters that can affect objects which completely exceed the logical foundations of High 1-A, much like it exceeds the ones defining 1-A and below, meaning that all possible levels of High 1-A are exceeded, even an infinite or uncountably amount of such levels. This tier has no true endpoint, and can be extended to any higher level just like the ones above.

Being "omnipotent" or any similar reasoning is not nearly enough to reach this tier on its own; however, such statements can be used as supporting evidence in conjunction with more substantial information.

 

[Antvasima]

Thank you very much for helping out. It is very appreciated.

Your suggestions largely seem good to me, but shouldn't we define tier 0 a bit clearer in mathematical terms?

 

[The_Impress]

Don't think Tier 0 is mathematically defined, unless I'm mistaken

 

[Antvasima]

I think that we have defined it by some higher level inaccessible cardinals previously.

 

[KingPin0422]

Even just the amount of infinite cardinals between the first inaccessible cardinal and aleph-2 (Which defines 1-A) is greater than cardinals such as aleph-0, aleph-1, aleph-2, aleph-3,... or even many alephs whose index in itself is an infinite number of cardinals.

I'd change this to something like:

Even just the amount of infinite cardinals between the first inaccessible cardinal and aleph-2 (Which defines 1-A) is greater than cardinals such as aleph-0, aleph-1, aleph-2, aleph-3, etc., and even many aleph numbers whose index is an infinite ordinal.

I also don't think the "uncountably infinite" part of tier 0's description is necessary, since I'm sure that even casual users can piece together that "infinite" includes "uncountably infinite" from context.

 

[Antvasima]

@DontTalkDT @Ultima_Reality

What do you think about the suggestions in the last posts?

 

[Antvasima]

@DontTalkDT @Ultima_Reality @KingPin0422

It is extremely important that we finish this.

 

[DontTalkDT]

For the time being I'm ok with Ultima's draft, with KingPin's revision thereof.

 

[Antvasima]

Thank you. That can probably be applied then.

However, it would be good if you together figure out the mathematical definition for tier 0, so it can be better explained in the page before we end this discussion thread.

 

[Theoretical_Toxic19]

Thank you. That can probably be applied then.

However, it would be good if you together figure out the mathematical definition for tier 0, so it can be better explained in the page before we end this discussion thread.

I'm not really here to add anything but just wanna get clarification on something since I haven't followed up on this thread in a while what's gonna happen to characters who reached atleast baseline Outerversal by transcending "all extensions of space time" without the existence of infinity layered hierarchies within their own setting are they gonna remain as outerversal or something what tier would be assigned to the totality of space time since currently 1-A in the tiering system only talks ab the cardinalities representing those tiers but doesn't mention anything about transcending concepts (all extensions) of space time

 

[Antvasima]

For the time being I'm ok with Ultima's draft, with KingPin's revision thereof.

Thank you. That can probably be applied then.

However, it would be good if you together figure out the mathematical definition for tier 0, so it can be better explained in the page before we end this discussion thread.

@DontTalkDT @Ultima_Reality @KingPin0422

 

[Antvasima]

@DontTalkDT @Ultima_Reality @KingPin0422

This is still an extremely important revision to finish.

 

[Antvasima]

@DontTalkDT @Ultima_Reality @KingPin0422

Are any of you willing to apply what has been decided here please?

Also, do you have any suggestion for how we should properly define tier 0?