Hello everyone, Son Raon here and I'm back with another chapter of my verse's Composite Cosmology known as the Raonverse.

In this chapter as the title suggests we'll prove - well... as egotistical as it may be, it's mostly I the one who's going to explain it since I'm the author of this book - the existence of a Type IV Multiverse in Raonverse, but before we get to that, let me clarify some things that I may have completely disregarded from previous chapters :

- For starters theories like Neoplatonism, Platonism (not counting the Platonic Concepts since although they are following the Theory of Forms by Plato) etc. can be used in scaling if enough context is provided.

The context itself that I'm referring to is the existence of mathematics and mathematical based scaling within the verse and what better way to explain it than trying to prove the existence of a mathematical Multiverse.
In other words, every time you're going to see me telling you about theories like Platonism, Mathematical Platonism - I have neither made up the term in my mind and Neoplatonism

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- All Normal Dimensions (or in other words lesser dimensions) of the Raonverse contain both spatial and temporal coordinates and are infinite in size. That's on top of the fact that the sub dimensions have an Aleph gap between them.

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- As far as how the overall scaling of the verse will go once it's over, I'll obviously rescale the entire verse itself once we're finished by proving the Type IV Multiverse since it'll have some... for lack of a better term implications in the scaling of the verse itself due to the existence of Modal Realism and Extended Modal Realism.

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- In case some of you are wondering if fully proving a Type IV Multiverse is going to affect the atom scaling of the verse, the answer to that is a resounding yes due to mostly the fact that I'm planning on reworking the atom scaling in order to be made more effective in scaling, overall narrative of my stories and in order to be easier to understand.

Unfortunately enough, that chapter will come much later since I've yet to reveal sertain things about the verse itself.

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- Finally, some parts of the verse are going to have different names which was needed since I wouldn't like anyone - including myself - to do a Nominal Fallacy (a.k.a Argument via Misinterpretation) due to the fact that some places in the verse have the same name.

The places that are going to change name are as follows :

A) The Composite Living World changing it's name to Mundus (=Latin for world) so that's different from the actual Living World which is the Type IV Multiverse that we're going to prove right now.

Now the main question that you may have in mind in regards to this may be : "Will this affect everything I've mentioned about the Algebrical Dimensions / Algebrical Dimensional barriers?".

The answer to that question is also a yes but as to how it'll affect them will be revealed in this chapter.

B) The Transfinite Dimensional gaps between the Minor Realms in the Planetary and Stellar cosmology which are going to be known from here on as The Three Voids.
Why three you may ask?
That's because there is :

i) One that is between the Mental Realm and the Ignis Realm, known as the Inner Void.

ii) One that is between the Ignis Realm and the Aqueous Realm, known as the Middle Void.

iii) One that is between the Aqueous Realm and the Nyx Realm that's known as the Outer Void (not to be confused with the scaling terms Outerversal)

C) The Otherworld will be known as Externus Mundus (a.k.a Outer World in Latin since the afterlife in my stories is by definition a place outside the world of the living, therefore naming it as Outer World it's a better and more closer to my In Verse terpretation)

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Now enough with my extensive parenthesis on things that I've forgotten to mention in previous chapters of my cosmology book and let's move on with the main dish of proving the Type IV Multiverse.

First of all, before I try to prove this Multiversal structure, let me refresh your memory and my own on the definition of what the heck is a Type IV Multiverse.

Type IV Multiverse, else known in the cosmological branch of metaphysics as Ultimate Ensemble, Mathematical Reality, Mathematical Multiverse and many more fancy names on top of it was a theoretical cosmological prototype that was proposed by the cosmologist Max Tegmark as a part of his Multiversal Theory known as M Theory.

Tegmark himself had stated that according to the M Theory, the Type IV Multiverse is in layman's terms the Final Frontier a.k.a the last type of Multiverse, meaning that any higher type of Multiverse like Type V, Type VI and higher is impossible to exist.

According to what Tegmark says a Type IV Multiverse is the theoretical, Multiversal model where a Type IV Multiverse would reside is one where the basis of the Theory Of Everything can be proven via Set Theoretical Framework a.k.a via the rules imposed on by Set Theory, more specifically Zermelo - Fraenkel Set Theory with the Axiom of Choice, mostly abbreviated in advanced mathematics such as ZFC Set Theory. In other words a universe where every mathematical law, conjecture, axiom and theory that exist in a universe as part of a total Mathematical Democracy is a Type IV Multiverse. In other words if Set Theory is proven and can work in a verse along with the existence of mathematics in physical form is what's necessary in order to prove a Type IV Multiverse via Tegmark's words.

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In terms of everything that makes up the theoretical framework of a Type IV Multiverse, Tegmark has clearly stated a lot of things - given the fact that he had written an entire book about it - but the main things that he said about proving it in accordance to Tegmark's books can be summarized in the following two parts which I'll explain in detail in order for you to understand them and for me to prove them without falling under Hitchens Razor Fallacy (a.k.a Burden of Proof Fallacy).

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The first thing that Max Tegmark had said about proving the infamous Type IV Multiverse as I stated before in my short explanation about the Type IV Multiverse is the Mathematical Democracy.

Mathematical Democracy in mathematics literally means that every mathematical construct, proven or not exist within the boundaries of a Type IV Multiverse. This includes, but it's not only limited to :

- Existence of Cardinals (Aleph Cardinals, Inaccessible, Woodin, Mahlo etc)

- Existence of Axioms (for example the Axiom of Choice, the Rank Into Rank Axioms etc)

- Existence of Conjectures (example of which being the infamous V=Ultimate L Conjecture)

- Theorems (for example Cantor's Mathematical Theory of Absolute Infinity, Cantor's Attic Theory etc)

In other words every type of mathematics ranging from Proven, yet to be Proven and non Proven via current mathematical knowledge / theories (a.k.a theoretical mathematical concepts) are needed to exist in order for the proven existence of a Mathematical Democracy.

Do you know what's funny about it? It's already proven to exist in the verse.

The reason behind it being the Algebrical Dimensions / Algebrical Dimensional Barriers that were placed at the quote-on-quote "edge" of the Living World (not to be confused with Mundus, a.k.a the cosmological structure known previously as the Composite Living World).

Within even the lowest those very "dimensions" (emphasis on the quotations since calling them dimensions isn't the best word to explain them in depth. Please let me know if you'd like me to make a chapter based solely on them) exist every single theorem, every single cardinal, every single principle and in other words - in order for me to not have to say more about every term in mathematics - exist in physical form.

In other words, even the lowest of those Algebrical "Dimensional" Barriers contains within it a full scale Mathematical Democracy in physical form.

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Now moving to the second part. The second part in proving a Type IV Multiverse according to the cosmologist's Max Tegmark's M Theory is to prove the existence of Set Theory itself in the verse in question.

The existence of which is also proven due to the R>F Hierarchy system I've been using through the book. The Axiom Of Inaccessibles.

By Axiom of Inaccessibles I basically meant the small theorem that I used in order to explain how much higher in the overall... for lack of a better term "food chain" of the cosmology I have placed its many layers of existence.

This theorem goes as follows : "Similarly to how you can't be finite levels over Infinity you can't be considered finite levels above something you transcend to the point of it being inaccessible.". This quote-on-quote "axiom" is quite literally and figuratively ZFC Set Theory in a nutshell.

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Now I know that many of you probably still have questions about it so allow me to explain it to you via a simple mathematical example :

Imagine now that you have a set of all Odd Numbers or S.O for abbreviation in one hand.

By definition Odd Numbers are numbers that can't be divided by two without having a number with decimal points as a result.

A sub example of which being the number three since this number divided by two gives us the number one point five.

Now due to the fact that ordinal arithmetic sequence is practically infinite, those odd numbers are practically infinite by themselves.

Additionally, imagine that you have a set of all Even Numbers in your other hand. I will abbreviate it with the term S.E. in order to avoid confusion.

The Even numbers by term are completely opposite of what the Odd numbers are since an Even Number is a number that can divided by two and having the result of giving us a number without decimal points.

Even Numbers are also infinite by definition due to ordinal arithmetic as mentioned beforehand.

Now imagine that you combine those sets in order to form the Set of All Ordinals - abbreviated as SoAO for obvious reasons - in the following equation :

S.O. + S.E. =???

Now allow me to ask you a question before we go further.

What do you think hides behind the three question marks?

If your answer is the SoAO (a.k.a Set of All Ordinals), you're partially correct and partially wrong.

Why's that?

That's because although it's true that SoAO hides behind the three question marks, you're also wrong since the SoAO is much bigger than the total sum of S.E. + S.O. that's because of the fact that in SoAO are included theoretical numbers that are considered impossible via ordinal arithmetic and numbers that aren't parts of either S.O or S.E.

If your answer was what I've stated then congratulations, you've learned what's Set Theory in a nutshell.

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Set Theory itself though can get even higher than that since even Cardinal numbers and arithmetic can be put in a quote-on-quote "tier list" due to the principle of Set Theory.

How does Set Theory work on scaling and cosmology?

It works with sets, albeit those sets are sets of worlds or dimensions, not mathematical numbers.

This is also where the term R>F Transcendence (a.k.a Reality>Fiction Transcendence) came from since in cosmology a plane that's higher due to concept of Set Theory than another would basically see the one below it similarly to how someone could see a comic book character.

If this sounds mind boggling, imagine how it looks like for characters since in powerscaling we're basically using characters, but in a different spectrum since there are two factors :

A) Existential Dimensionality : Where a higher is in a higher dimensional plane than the other.
Two examples of which come from DC comics. One being when Orion brought Superman in the God Sphere and said to Superman that the universe they were into was as irrelevant as a microbe compared to them :

And the explanation of Quantum Superman (a.k.a Captain Allen Atom) to how a three dimensional world looks to him :

A character with higher dimensional existence moving into a three dimensional plane under realistic circumstances would be destructive, but in many verses there are rules that beings of that level need to attain a lower dimensional form in order to be perceived by the beings of the lower dimensions.

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B) Dimensionality via feats : Dimensionality via scaling is an entirely different thing than dimensionality via existence.

Dimensionality via feats is mostly due to the Attack Potency/Destructive Capacity of a character. Abilities and feats aren't counted since there are characters like Rimuru from Tensei Shittara Slime Datta Ken who has Dimensional Manipulation as a power, although in terms of AP and DC he's just Multiversal due to effortlessly destroying ten thousand universes due to seeing a nightmare.

One actual example of dimensionality via attack potency is a character who's capable of destroying a Universe+ structure. Characters of those caliber get an infinite fourth dimensional attack potency (since the dimensions in an infinite universe are : Three spatial (length, width and depth) and one temporal) which would make them qualitatively superior in terms of scaling to a character who's let's say able to casually destroy a finite observable universe since destroying a finite fourth dimensional universe - a.k.a the observable universe - would logically scale lower than an infinite universe.

Dimensionality via AP doesn't only show the strength of a sertain character since it also showcases :

- It's durability due to the fact that it scales to the character's AP and DC

- The Speed since if in the verse the speed increases in connection to strength, a character being able to destroy a fourth dimensional infinite universe would scale off of the created shockwaves and have infinite speed due to destroying something infinite in finite time.

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The third part is to explain that a physical Type III Multiverse (a.k.a a Quantum Multiverse) is a Mathematical Structure.

This had been proven easily mainly due to the fact that within the boundaries of the Algebrical Dimensions exist all other types of Multiversal structures, including Type III as I explained in earlier chapters about the Multiversal scaling.

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Now that we've proven a Type IV Multiverse in Raonverse via Tegmark, let's see what's necessary in order to prove it by more deeply scaling measurements.

The scaling measurements that I'm going to use will be found in the pinned comment of this video with the title : Type 4 Multiverse Explained (Beyond Boundless EP:1)

https://www.youtube.com/watch?v=UacT9YbwCyg

According to the video above, in order to prove a Type IV Multiverse in a more scaling perspective you have to explain :

- Existence of Metaphysics as a variable

- Existence of Set Theory as a fundamental of the verse.

- Existence of Layers of Metaphysics as a Variable.

I'm not going to lie to you this is going to be the fastest one so far since :

- Set Theory was already proven both as a fundamental part of the verse and a variable via the extended usage of the Axiom of Inaccessibles.

- Metaphysics are a variable in the Raonverse, because of the fact that there are many abstract, metaphysical planes in the verse itself. Those metaphysical planes are as of currently seen in the planetary and stelar cosmology of the verse (Mental or Nous, Ignis or Phoenix Crown, Aqueous Realm or Ocean of Dreams, Nyx Realm or One Star and the Three Inner Voids).

- The layers of metaphysics are also proven by extension due to the many layers those metaphysical realms have.

Now the million dollar questions.

First of all, where does the Type IV Multiverse scale in conjunction with Set Theory?

The answer is found in this video with the title : The Journey from Tier 12 to Tier 0 [Powerscaling] by Project FM which is the most accurate one I can find since it also states where the Type IV Multiverse actually scales at in comparison to the prior video.

https://www.youtube.com/watch?v=SyyOJ3qbw30

This video is also the tiering system I use in terms of scaling since it's the most complete and well explained one I've found

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Now comes the second question, what kind of... for lack of a better term "repercussions" would the proven Type IV Multiverse have for my verse?

The only repercussions it'll have is a scaling headache for me as a scaler due to the fact that Modal Realism, Extended Modal Realism and Bohm's Theory exist as parts of the verse.

In case some of you don't remember let me give you a re introduction to them.

Let's start by Modal Realism since it's the easiest to explain. Modal Realism as explained by the cosmologist David Lewis is a theorem that says that there exist many possible worlds similar to ours and follow four "tenets" :

- The term actual world is indexial, meaning that any being no matter their place can say that their world is the actual one, they mean their world. For example think about beings that are from different multiverses in fiction when they say their world, it's in other words the Multiverse they originated from.

- Possible Worlds Exist and are as real as our world. In other terms if a verse has a Type IV Multiverse in them and Modal Realism, there would be multiple of them existing, although separated from one another for obvious consistency issues.

- Each possible world is spatiotemporally and causally isolated from the other. Meaning that if in the verse's lore there are no ways of getting from one possible world to another, the worlds themselves can exist, but will be isolated from one another in terms of existence.

- Possible Worlds can't be reduced to anything more fundamental - they're irreducible cosmological entities and structures in their own rights. Although this part may debunk the entire idea of type IV Multiverses and Modal Realism working together as a consistent totality, it can be easily subverted due to theories like Extended Modal Realism.

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Now some of you may ask as to what I mean by possible worlds? Possible Worlds by definition fall under the Theory of Possible Worlds by the Cosmologist Leibniz on his studies about the necessity, actuality and existence of possible worlds. In other words according to Leibniz, possible worlds are both figuratively and literally infinite worlds that some of them exist "near" to what we defined previously as actual world through examples and some other exist "further" away.

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Now to Extended Modal Realism. Extended Modal Realism is a variation of Modal Realism proposed by the cosmologist Takashi Yagisawa.

In his version of Modal Realism, Yagisawa aimed to extend the David Lewis' theory of Modal Realism in order to include possible and impossible worlds. Modal worlds are in a sense modal dimensions and there's only one true world/reality.

A unified reality where the actual, the possible and the impossible are one and connected.

In layman's terms, Impossible Worlds are worlds without contradiction. In order to give you to understand what I mean by that I'll do you a question.

Remember what I said previously at the fact that the possible worlds of modal realism are irreducible cosmological entities or structures?

Well that irreducible entities/worlds contradiction means nothing in the face of External Modal Realism due to the fact that although it'd be contradictory by only Modal Realism as the logical basis for possible worlds to reduce in more fundamental forms, in Extended Modal Realism there's no such worry.

In other words if let's say we had a cosmology in fiction that has Type IV Multiverse and Extended Modal Realism as their main tools, the existence of a Type IV Multiverse would be everywhere within the cosmology, from its universes to it's atoms.

Or allow me to give you a simpler example. In verses that have proven Extended Modal Realism, existence of smaller cosmological prototypes like the black hole cosmology (a.k.a a cosmological prototype theory where the observable universe exists within the center of a black hole) would be an existing thing and no one would bat an eye.

Or another example, imagine a cosmology with universes existing encapsulated within its atoms, if that cosmology follows Extended Modal Realism, this isn't contradictory at all.

What I'm trying to help you understand is that in Extended Modal Realism, contradictions are essentially illusions due to the fact that contradictions happen due to logical impossibilities and logical impossibilities exist within the Extended Modal Realism itself.

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Last theory for today is David Bohm's Bohm Theory. The Theory of Implicate and Explicate Order is a theory provided by the quantum David Bohm, trying to find a reconciliation or in other words a "meeting point" between the principles of Taoism and Metaphysics.

A summary of this theory is as follows :

"There are two orders in this world, the Implicate and the Explicate. From them the Explicate or Exfolded Order are the ordinary notions or in other words phenomena that we can see and explain whilst the enfolded or Implicate Order is phenomena that we can't see and explain via normal means, but with deeper intuition."

In order to understand it let's take the relationship between quantum physics and the concepts of space, time and reality.

The atomic position in the subatomic... for lack of a better term canvas gives us the position of something on someone in space, the movement of these molecules gives us time whilst the total interactions of both give us the reality we live in.

In powerscaling, Bohm's theory can be used to explain cosmological things that most people would think as impossible.

For example, let's take Dr Manhattan vs every magician in DC during the events of Doomsday Clock comic book issues.

Manhattan flat out told them that what they call as magic is basically discarded remnants of reality and you know what reality is composed off of via what we've said before about the corelation between reality, space and time along with the quantum physics.

This also proves as to why Quantum Manipulation as a superpower is insanely powerful even in a fictional standard.

Or let me give you another example, even simpler this time. Let's take for example a verse where magic and science are the same thing.

Why doesn't magic and reality being the same thing doesn't seem controversial via powerscaling?

In the terms of sciences what people of the past called magic is basically what the scientific progress of that era didn't manage to explain properly.

This means that by Bohm's Theory the Explicate order (a.k.a the proven and tested order) is magic whilst the Implicate order (a.k.a the non proven, intuitive order) is science as explained perfectly according to the following saying :

"One worlds science is another world's magic".

Now to explain further the connection of what we've said about Bohm's Theory with theories like Type IV Multiverse, Modal Realism and Extended Modal Realism we've got the following :

- Type IV Multiverse exists.

- Modal Realism allows the existence of infinite of them in conjecture with Leibniz's Possible Worlds Theory, but in the same time debunks them due to the irreducible entities tenet.

- The irreducible entities tenet debunk becomes easily a logical fallacy not meant to be taken seriously due to Extended Modal Realism's impossible worlds that allow it since irreducibility is a contradiction to reducibility and due to the fact that EMR throws contradictions out of the window, the Type IV Multiverses can exist and still be capable of being reduced.

- Type IV Multiverses can exist in places like the planetary/stellar cosmologies or even more extremely in atoms due to although not proven by explicate order, the implicate order still allows their existence in tandem with EMR

Conclusion : Every universe statements in the Raonverse is an amalgamation of Type IV Multiverses

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That's all I had to say about this cosmology chapter. In the next chapter we're going to scale thoroughly the entire verse via Project FM's Tiering System video and see how high in the tiering system is a semi complete universal construct of the Raonverse in full scale.

I hope that all of you will enjoy reading this chapter as much as I enjoy writing it and I hope to find you in the other books of mine with other chapters later on.

Raon out.