Infinitely increasing attributes, I dominate the multiverse Chapter 677 Super-class self-reference,

After reading all the memories of Yun Zun, Mu Cang learned.

In fact, the mysterious and powerful Dao Master clan, in a sense, should be called "super-class species" or "super-class civilization", rather than the so-called "super-true species" which is more vague in definition.

Because the concept of "super-class" with a strong self-referential nature actually means... "everything outside of everything".

And the Dao Master clan is just a powerful species that exists outside all von Neumann universes V with different strengths, or all different levels and types of universal mathematical logic territories.

The so-called universal mathematical logic territory can usually be called the universal mathematical universe.

It refers to a large class of cornerstone universe models that can greatly accommodate the universality of various mathematical models, and can fully satisfy the complete saturation of various properties of various mathematical models, and can ensure that all levels of subset structures in all mathematical models can be symmetrically fully expanded and embedded in the homogeneity of all models.

As for the so-called self-reference mentioned earlier, it can also be called self-referential feedback or recursive self-reference. Its essence is that a certain concept, idea, sentence, theory or even entity, etc., refers to itself, describes itself, and shows itself in itself.

To put it more simply, the content of the proposition is the proposition itself, or is related to itself.

For example:

[This sentence is very short][I am the subject of this sentence][This sentence has seven words][Everything is absolutely wrong][This sentence is self-referential][It says that this sentence is this]... and so on.

However, self-reference usually brings many logical contradictions and endless recursion and backtracking, which then creates various difficult circular paradoxes.

For example, if a sentence claims to be a lie, is it true or false?

It's very contradictory.

And to achieve self-reference, you need to have a self-referential structure.

Generally speaking, a self-referential structure refers to a structure that can use itself as a component of itself.

In terms of logic and entity, it is usually a wonderful circular structure, and then through the perpetual self-referencing, a part of itself will eventually point to itself.

This kind of circular self-referencing structure can be roughly divided into two categories.

1. Incomplete self-referencing structure: a structure with contradictions or paradoxes that cannot be fully described, developed and presented in its own system of symbols, logic, concepts and entities.

This structure is also an important premise of Gödel's incompleteness theorem - [there are always unprovable true propositions in the mathematical system] and Hilbert's undecidability theorem - [there are certain propositions that cannot be proved or denied by their own proof methods in the mathematical system].

2. Complete self-referencing structure: a perfect structure without any contradictions or paradoxes, which can be fully described, developed and presented in its own system of symbols, logic, concepts and entities.

The group of masters to whom Yun Zun belongs is precisely a super civilization with a perfect and complete self-referencing structure.

The power of this super-species lies in the fact that they all possess a miraculous power called "Universal Principle", or... core endowment.

Under the influence of this core endowment of "Universal Principle", any perfect master of the Dao... is the so-called True Master.

No matter where he arrives and enters any universal logic territory ruled by any background axiom, he can perfectly embed his own essence into the background axiom system of the territory and quickly gain the highest dominant position of the system.

For example, if a True Master suddenly descended into the True Universe where Mu Cang is at this moment.

Then after this true palm descends, the Zerlo Fraenkel axiom set theory system, which is composed of the extension axiom, disordered pair axiom, regularity axiom, classification axiom, subset axiom, power set axiom, pairing axiom, union axiom, substitution axiom, infinity axiom, choice axiom, well-ordered axiom, empty set axiom, etc., which truly rules this universal universe, will become his body and flesh in an instant because of the power of the "universal truth", and be driven by him as if he were using his arms.

At that time, all the entities corresponding to the transfinite cardinality under the ZFC axiom system that constructs and exists in this true class universe, whether this entity is a life with thinking and wisdom, or a phenomenon without wisdom and knowledge, or a realm that carries life and phenomena, will unconditionally crawl at the feet of this true palm, and be enslaved, trampled, disassembled, reconstructed, defined and destroyed without any resistance.

If the True Palm is willing, He can even modify and reshape the entire ZFC background axiom system easily by driving the "Universal Principle", so as to make ω1 Aleph one, or make ε0 Aleph infinite, or even make the real number set R? fixed point, or even make the power set of the real number set R = PA fixed point.

In short, all phenomena, concepts, and logic that all intellectual life can understand and experience are equivalent to toys that can be manipulated and ravaged at will for the True Palm.

This is the power of the True Palm.

What infinite creatures, what super-poor life, what Aleph family, in front of any True Palm, will not be more powerful than any small carbon-based paramecium, and are all insignificant little ants.

In addition, like the previous luck master, the reason why he is able to instantly possess the base level strength corresponding to that realm every time he reaches a realm actually relies on this innate ability.

However, because Yun Zun is a master who has suffered severe injuries and has subsequently deteriorated to the level of a pseudo-hand, he is simply unable to fully embed himself into the ZFC background axiom system of this territory, so he is unable to exert his "universal power". The true power of "reason" --\u003e\u003e

quantity.

But even so, Yun Zun can still easily display a power effect similar to Mu Cang's heaven-defying skill [I can get it when I see it].

All I can say is that the power of the "universal principle"... is really too terrifying.

But what's even more outrageous is that this terrifying power that can arbitrarily dominate any mathematical background axiom system is not the strongest endowment of the Taoist family. At best, it can only be regarded as their basic ability.

According to the records of Yun Zun's memory messages, the true strongest power of the Taoist clan is actually a core talent called "Ancient Mysterious Essence".

This endowment has no other redundant functions. It has one and only one ability.

The specific power effect of this ability is...

It allows the master to 'incarnate' into a 'vessel' with a powerful recording function, to imitate and load one or more large cardinal axioms... such as the overall logical structure model of "unreachable cardinal numbers", and turn it into Its own internal component - "mysterious marrow", and then use the "mysterious marrow" as the foundation core to reconstruct the ontology, and then evolve into a terrifying large cardinal life form.

That is the so-called... Xuan Marrow level master, referred to as "Xuan Zhang".

What needs to be known is that although the strength of the axiom of large cardinality is high, it can often be regarded as zero after crossing boundaries.

Another thing that needs to be known is that after becoming a real big cardinal life form - Xuanzhang, the master still has the innate ability of "Universal Principle" whose structure and principle are both a mystery.

And by using this ability, Xuanzhang can perfectly exert all the power of its Xuanmian cardinal number in any universal mathematical universe or other types of mathematical realms governed by any background axiom system. able.

In general, compared with the real palm, the fake palm with an ability similar to "See and I get it" is about zero.

The real palm, which is equivalent to the Almighty God of Von Neumann's universe, is as small as zero compared to the mysterious palm.

Because all 'blank slate' true-like universes composed of all cardinal numbers; and all set-theoretic multiverses with multiple mathematical structures, rules, logics, and constructability standards; and all von Neumann's special expansion forms The universe is deeply involved in the special complex universe in the fields of model theory and forcing logic; it is even a larger complex universe, and even a larger Vlogic logical multiverse. Compared with any large cardinality, even with the so-called Compared with the 'minimum' big base number - the world's base number, they are as small and humble as dust.

No, even dust is far inferior, it can almost be regarded as zero.

As for the word 'blank slate' mentioned in the passage about the so-called 'blank slate' true type universe, it refers to any true type or von Neumann universe V. In fact, it can also be like the master of the path. That way, one or more large cardinality axioms are 'loaded' into itself.

Once one or more large cardinality axioms are 'loaded', and these axioms do not conflict with each other, then the strength of the von Neumann universe V will take off instantly and become a more powerful universe in a popular sense. It is a higher-order true-like universe.

And because there are many types of large cardinal numbers and there are huge differences between them, the von Neumann universe V of different levels will also be vastly different.

However, once a mysterious marrow-level master accidentally loses his marrow component - the large cardinal axiom logical structure model due to various reasons, then his various core talents will also be severely damaged, and then deteriorate tragically. The so-called "pseudo palm".

It can be said that almost all pseudo-palms are such unlucky people.

For example, Yun Zun is like this.

According to the records in his memory, his original marrow was the logical configuration of "World Cardinality", which can be abbreviated as WC.

The so-called world cardinality, its basic definition is:

If Vα is the model of ZFC, then α is a world cardinality. Meet VκZFC

Of course, if this seemingly simple definition is fully expanded, it will be extremely lengthy, boring and difficult.

For this, you only need to know that the mysterious element of the Master of Fortune is actually not the low-level 2WC that contains unlimited WC, nor the slightly higher-level 3WC that contains unlimited 2WC, but the KWC at the fixed point level. World base.

Like the Aleph fixed point, the pa fixed point and the PA fixed point, there are endless fixed points 'inside' the world base, and the KWC base is the first fixed point.

As for the unreachable cardinality above this, we can only say that if it completely satisfies the WC world cardinality, there are unbounded many "inside" it.

The so-called "unbounded" means that there is neither an upper bound nor a lower bound within the definition domain. It is so huge that there is no restriction at all. Anyway, you can stuff it in as much as you want. As long as it does not reach the unreachable cardinal level, it will always be stuffed. dissatisfied.

From this, we can see how huge the unreachable base is. It is the other side of heaven that all small intellectual beings exhaust their imaginations and are far...far beyond the reach of.

Let alone the lofty unreachable cardinality, even if it is the complete state of Yun Zun who possesses the world cardinality-level Xuansui component, how powerful it is, to be honest, Mu Cang can't imagine it at the moment.

He can only roughly think that the entire universal mathematical universe he is in now, if compared with the real Xuan Zhang version of Yun Zun, is probably as small as zero.

And the enemy who caused Yun Zun to fall from the Xuan Zhang to the pseudo-Zhan level and imprisoned him in the prison of ? is precisely one of his unreachable cardinality-level fellows-an unknown Xuan Zhang named "Pete Tianwang".

Regarding the intelligence information of this Xuan Zhang, Yun Zun's memory is inexplicably blank, without any useful information, only a large amount of emotional torrents filled with strong hatred, pain and humiliation.

I don't know what this Peter Tianwang did to make Yun Zun hate him so much, and it was so humiliating and painful.

Could it be that this King Peter… has also used similar ultimate insults or even more terrible means to ‘entertain’ Yun Zun?

--\u003e\u003e

Mu Cang, no way of knowing.

“So…”

Mu Cang said to himself leisurely, “I should try to return to the True Palm level first, then find a True Class Territory with a large cardinality structure level to enter it, and then use my innate ability to copy the large cardinality logical configuration contained in it, complete the body reshaping, and then advance to the Xuansui level True Palm.”

Obviously, this is Mu Cang’s next plan.

As for the hatred between Yun Zun and King Peter… what does that have to do with Him? Inexplicable.

In short, while the ‘loophole portal’ has not been fully constructed, Mu Cang immediately activated [Ling Yue Fei Fei].

Start trying to see if you can return to the True Palm level.

Activation effect——

〈At this moment, I am a pseudo-palm with all incomplete talents ≠The next moment, I am not a true palm with all perfect talents〉

Buzz——

In an instant, Mu Cang's entire body and soul suddenly became blurred, as if it was about to be scattered among the infinite universes.

Then, just a moment later, his body and soul suddenly stabilized, as if nothing had happened.

But only Mu Cang knew that he... succeeded, and successfully rose from a pseudo-palm to a true palm level.

At this moment, if he wanted, he could completely embed himself into the ZFC background axiom system of this true class territory, and then obtain the highest dominance of the entire axiom system, and then redefine this von Neumann universe into another form.