Infinitely increasing attributes, I dominate the multiverse Chapter 695 Ikaros, soaring into the sky

Mu Cang even guessed.

Maybe, King Peter is the same as him.

In the beginning, he was just an ordinary earthling.

It was only because he accidentally obtained the final fragment that he rose to great heights, cheated all the way and finally became an immortal.

"However, when I captured the clone of King Peter, I didn't feel any intimidation. Could it be because..."

Mu Cang thought deeply, "Is it because of the chaos of chaos?"

If this is the case, then it is understandable.

Because Mu Cang already knew it a long, long time ago.

For example, [See is what I get], [Ling Yue Feifu], [Infinite Secret Strategy], and perhaps [Domination Invasion] from King Peter.

These final fragments and the chaos of chaos actually belong to the same "series" and are part of the same divine object.

It's just that among these fragments, only Chaos's Delusion is the core of the core, part of the basic main part, while the other fragments belong to the branch parts. (See Chapter 620 for details)

As secondary parts, these fragments can only be unsealed and release their true power after being integrated with the main part, Chaos Delusion.

Just like King Silver Horn's female purple gold gourd, when she saw the male purple gold gourd of Monkey King, the Monkey King, her magical powers were suddenly greatly reduced.

Perhaps it was precisely because of this relationship of one male and one female that the [Domination Invasion] of King Peter failed to have the desired effect on Mu Cang.

In addition to this, Mu Cang also thought of a possible reason why the clone of King Peter did not initiate the body seizure after being interfered by him.

That is, could it be that the number of bodies taken by King Peter... has reached the upper limit?

There is a certain possibility.

"By the way, why wasn't Yun Zun taken away by King Pit? Instead, he defeated Xuan Mian and became a fake palm?"

With this question in mind, Mu Cang immediately activated [Ling Yue Feifu] again... No, he activated this skill many times, and around the heaven-defying ability of [Domination Invasion], he started various "void attacks" Ask a question."

Later, after many "questions", Mu Cang gradually understood the mystery.

In other words, it further completes the specific details of the power effect of the heaven-defying skill [Domination Invasion].

In short, according to the answers to the "Void Question", it can be seen that King Peter can indeed do it. When he senses and interferes with others, and when he is sensed and interfered by others, he immediately and automatically seizes the body.

But this function, King Peter himself... can actually reset it automatically.

In other words, King Peter can take his body when he wants, or not if he doesn't want to. He can even take only half of his body, making the other person become a part of him, but he doesn't know that he has been taken away.

By analogy, it's as if King Pete as a whole belongs to a super hacker, while those non-staff individuals who have encountered half-inhabited homes belong to cyber broilers or backup broilers.

This is obviously much freer than "I'll get it when I see it".

To be honest, [See It, I Get It] is just a bit too overbearing. He only plays forced love. He doesn’t ask whether Mu Cang wants to become stronger or not. He just pulls him hard when he gets the chance. He flies.

It’s very tiring to fly all the time, okay?

In addition, Mu Cang also learned from the information obtained from the "Void Question" that King Peter's current strategy for seizing the body is very likely to... value the essence rather than the wealth.

That is, only those individuals whose strength is [super huge base number] will be captured, and those below this level will basically not be captured.

In this regard, Mu Cang guessed that the number of clones of King Peter might be the super huge base number itself, so he probably wouldn't care if tens of thousands, hundreds of millions or even infinites died.

If King Peter had a lazy character, he might not even take revenge.

Because for King Peter, as long as they are not super huge cardinal-level clones, even if those other low-level ones die infinitely, it will not be worse than losing a hair.

serious.

It can only be said that compared with super huge bases, measurable bases, Wuding bases, and ultra-compact bases are indeed weak.

As for how huge the super huge base is, this is another more complicated issue.

First of all, there are many huge high-order large cardinals between it and ultra-compact cardinals.

For example, a large cardinality that is "relatively close" to a supercompact cardinality is an extendable cardinality.

The fundamental definition and mathematical structure of this large base is... If a base δ is called extendable, then for each λ\u003eδ, there will be an initial segment Vλ with e\u003cλ, and a subsequent segment Vλ. The element embedding map π from Vλ to Ve satisfies the result that π(δ)=δ and π is not an identity map.

In plain language, this mathematical definition means that the expandable base can "stretch" into a universe model smaller than itself, while maintaining certain structural characteristics of its own.

Very magical.

In addition, the so-called "scalability" is exactly the second-order analogy of "strong compactness".

At the same time, except for the expandable base.

Under the super huge cardinal numbers, there are also huge cardinal numbers, almost huge cardinal numbers, and Wopenka's principle.

The so-called Wopenka principle is an important mathematical principle closely related to set theory, category theory, and model theory.

Its main content can be briefly summarized, that is, for any true class structure in some languages, there is an elementary embedding that can be embedded into another true class --\u003e\u003e

members within the structure.

Therefore, a series of properties about proper class structures and elementary embeddings can be derived through this principle.

These properties are related to unreachable cardinalities and their various applications in model theory.

Next, based on Wopenka's principle, is the almost huge base.

Theoretically speaking, if a base k is an almost huge base, then for any regular base λ\u003ek, there will be a λ-complete ultrafilter U on pk(λ), such that for any x?pk( λ).

At the same time, if x is true in U, then there will also be a function f:λ→k, so that for any a\u003cλ, Y will exist in x, so that Ynxa=?, and f "Y?xa.

It can be said that the properties of this almost huge cardinality are so powerful that it can even be used to deduce and prove the properties and consistency strength of many "smaller" large cardinals, such as measurable cardinals, strong cardinals, supercompact cardinals, and so on.

The mathematical essence of the huge cardinals located above the almost huge cardinals and below the super huge cardinals is... an elementary embedding j existing in V: V → from V to a transitive inner model with a critical point K.

The concept of "elementary embedding" mentioned here is simply a mapping defined between two set domains.

In other words, elementary embedding is a function that can maintain the structure of a set. It not only maintains the relationship between elements, but also maintains the relationship in logical form.

For example, given two sets and N, if there is a mapping j:→N, such that for any formula φ and parameter a in φ, φ[a] in N is true if and only if φ[j(a)] in N Established, then j can be said to be an elementary embedding from to N.

As for the mathematical structure of huge cardinal numbers, if a is a limit ordinal number such that a\u003e0, then it can be said that an uncountable regular base k is a-huge.

At the same time, if there is an increasing sequence with a base 〈k?:β＜a〉, then for all β＜a it is Vk??Vk.

Subsequently, if n\u003e1, and 〈β?:i＜n〉 is an increasing sequence of ordinal numbers less than a, then β?≠0, which means there is an elementary embedding j for all β"＜β?: Vk?????Vk????, and the critical points k?" and j(k?")=k?? and j(k??)=k????.

Then, if 0≤I\u003cn–2, and β?=0, then for all I, there will be a

The elementary embedding of critical point k"\u003ck? and j(k")=k? and j(k??)=k???? is j:Vk?????Vk????, thus making 0≤ I\u003cn–2.

Here, the concept of super huge cardinality can finally be introduced——

That is, if a base k is k-giant, it can be called a super-giant base.

Furthermore, a base k is called a super giant. If there is an elementary embedding from Vk to Vk, then Vk is the giant logical model composed of all sets with rank less than or equal to k.

The relationship between super giant, huge, and almost giant is - if k is a giant base, there is a regular ultrafilter U located on k, such that {a\u003ck|a-nearly giant base}∈ U; if k is a super huge base, then k is an extendable base, and there is a regular ultrafilter U on k, such that {a\u003ck|a-extendable base}∈U; if k is 2-huge The base, that is, there will be a regular ultrafilter U on k, such that {a\u003ck|Vk|=a-super large base}∈U.

At the same time, after reaching the level of huge cardinal numbers and super huge cardinal numbers, it will also be closely related to the axioms named I3, I2, I1 and I0.

The so-called axiom I3 is: there is a non-trivial basic embedding of Vλ into itself;

As for axiom I2, it is: V has a non-trivial basic embedding into the transitive class containing Vλ, where λ is the first fixed point above the critical point;

Axiom I1 is: non-trivial basic embedding of Vλ+1 to itself;

Axiom I0, that is: there is a non-trivial basic embedding of L(Vλ+1), and its critical point \u003cλ axiom.

The major axioms l3, l2, l1, and l0 all have different strengths of consistency.

The consistency strength of a-giant cardinal numbers and super-giant cardinal numbers with a limit ordinal number \u003e 0 is exactly between the l3 axiom and the I2 axiom.

There is also a variant of these axioms, which is also a large cardinality, that is... the Icarus cardinality.

The so-called Icarus base is... If there is a non-trivial basic embedding of L(V_λ+1, lcuras) with a critical point lower than λ, then Icarus exists in V_λ+2-L(V_λ+1) .

Then, if x is said to be an Icarus set, then if and only if Vλ+2 is the disjoint union of x and Y, then any y∈Y can be allowed.

At the same time, it can be proved that j: (Vλ+1, xu{y}) → (Vλ+1, xu{y}) is established.

Therefore, j:(Vλ+1,x)→(Vλ+1,x) is the most consistent embedding form compatible with the axiom of choice under j:Vλ+2→Vλ+2.

If you want to reach a higher level, you have to transcend the axiom of choice and touch the Reinhardt cardinality.

"So..."

Mu Cang's eyes flashed, "Is the total number of all the clones of King Peter... a super-huge cardinality?

If so, if I obtain the location information of all his clones through [Ling Yue Fei Fei], will I... also become a super-huge cardinality-level life?"

This idea feels worth trying.

So the next moment, Mu Cang activated [Ling Yue Fei Fei] and began to try to obtain the location information of all the clones of King Peter.

Buzz——

\u003c--\u003e\u003e

br\u003e    The fact is... Mu Cang succeeded!

Boom!

In an instant, an extremely huge, extremely grand, extremely vast, extremely vast, and extremely huge torrent of information appeared out of thin air in his heart and mind.

According to normal logic, Mu Cang would be forcibly broken, torn, wiped out, and evaporated into nothingness by this extremely boiling, surging, and passionate information torrent in the first place.

However, under the heaven-defying power of [Infinite Secret Strategy], this roaring and howling information torrent that seemed to destroy all phenomena, logic, and rules in the world was perfectly digested by Mu Cang in an instant.

And at the same moment of digesting this super-huge cardinality-level information torrent, Mu Cang's root essence, spiritual thinking, mysterious marrow, etc., and even everything, also seemed to completely surpass the super-compact cardinality, the Wopenka principle, the almost huge cardinality, the huge cardinality, and many other levels without any process, and stood firmly at the super-huge cardinality level.

After completing this shocking transformation, Mu Cang's eyes flickered slightly, and he instantly distorted the digital logic territory where he was, disrupted and reset it, and expanded it into a magnificent complex universe with a super-giant cardinality and grand logical structure.

"Hehe, it's true..."

Mu Cang raised his head and laughed, "Flying into the sky, breaking through the nine layers of the sky!"

After laughing, He instantly split into super-giant cardinality super-giant cardinality clones, stepped out of this huge complex universe, and killed the area where all the clones of King Peter were located.

Generally speaking, even if the master can unscrupulously clone, project, and map.

But because of the uniqueness of the mysterious marrow, they cannot really "create" a large cardinality-level external incarnation.

But Mu Cang is different.

He is a super-giant cardinality-level life that is perfect in all aspects, not those so-called mysterious palms that rely on the mysterious marrow to rise.

Therefore, as long as Mu Cang wants to, as long as he is willing, he can "create" all kinds of clones without any scruples and restrictions, and the magnitude and level of these clones can all be absolutely consistent with Him.

Free reading.