After reading all the memories of that Yun Zun, Mu Cang learned.
In fact, that mysterious and powerful family of Taoists should, in a sense, be called a "super species" or a "super civilization" rather than the so-called "super species" that is more vague in terms of definition.
True species".
Because "superclass", a concept with a strong self-referential nature, actually means... "everything outside of everything."
The Taoist group is precisely a powerful species that exists outside all von Neumann universes V with different strengths, or all different levels and types of universal logic.
The so-called universal mathematical realm can usually also be called the universal mathematical universe.
It refers to a large class of properties that can greatly accommodate a variety of mathematical models (universality), and can fully satisfy various mathematical models (saturation), and can ensure that all mathematical models have various properties.
The hierarchical subset structure can be fully extended and symmetrically embedded into the cornerstone universe model of each model (homogeneity).
As for the so-called self-reference mentioned earlier, it can also be called self-referential feedback or recursive self-reference. Its essence refers to a certain concept, idea, sentence, theory or even entity, etc., which refers to itself and describes itself.
, show yourself.
To put it simply, the content of a 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 that is absolute must be wrong] [This sentence is self-referential] [It is written like a sentence
This]...and so on.
However, self-reference usually brings about many logical contradictions and endless recursion and backtracking, thus creating various intractable circular paradoxes.
For example, if a statement claims to be false, is it true or false?
It's quite contradictory.
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.
At various levels, such as logic and entity, it is usually a wonderful circular structure, and then refers to itself through a continuous cycle, with a part of itself ultimately pointing to itself.
This kind of cyclic self-referential structure can be roughly divided into two types.
1. Incomplete self-referential structure: a structure with contradictions or paradoxes that cannot be fully described, developed and presented within its own system of symbols, logic, concepts and entities.
This structure is also Gödel's incompleteness theorem - [There are always unprovable true propositions in mathematical systems], and Hilbert's undecidability theorem - [There are certain propositions that cannot be proved by themselves in mathematical systems.
method to prove or deny] an important premise.
2. Complete self-referential structure: a perfect structure without any contradiction or paradox at all, which can be completely described, expanded and presented within its own system of symbols, logic, concepts and entities at all levels.
The group of masters that Yun Zun belongs to is precisely a super-civilization with a self-referential structure of perfect completeness.
The power of this super species is that each of them possesses a wonderful power called "Universal Principle", or... core talent.
Under the influence of this core endowment of "universal principle", any master who is in a perfect state...is the so-called true master.
No matter when it arrives and enters any universal logic territory governed by any background axiom, it can perfectly embed its own essence into the background axiom system of that territory, and quickly gain the highest dominant position in the system.
For example, at this moment, a true palm suddenly arrived in the true universe where Mu Cang is located.
So after the arrival of this true palm, what truly rules this universe is the axiom of extension, the axiom of disordered pairs, the axiom of regularity, the axiom of classification, the axiom of subsets, the axiom of power sets, the axioms of pairing, and the axiom of union.
The Zermelo-Fraenkel axiom set theory system (referred to as the ZFC background axiom) composed of all the axioms such as the axiom of substitution, the axiom of infinity, the axiom of choice, the axiom of good order, the axiom of the empty set, etc., will be in an instant because of the "universal axioms"
Caused by the power of "the Supreme Principle", it became His body and flesh, allowing it to be driven like an arm and a finger.
At that time, all the various entities corresponding to the transfinite cardinal numbers under the ZFC axiom system of the ZFC axiom system are constructing and existing in this square universe, whether this entity is a life with thinking and wisdom, or an unintelligible phenomenon, or it carries life and
All realms of events will unconditionally prostrate themselves at the feet of this true palm, without any ability to resist, allowing them to be enslaved, trampled, dismantled, reconstructed, defined and destroyed.
If this real palm is willing, he can even easily modify and reshape the entire ZFC background axiom system by driving the "Universal Principle", so that w 1 = Aleph one, or e0 = Aleph infinity
, or even let the real number set R = ? fixed point, or even let the power set of the real number set R = PA fixed point.
In short, all phenomena, concepts, and logic that all intellectual beings can understand and experience are equivalent to toys that can be played with and ravaged at will by Zhenzhang.
This is the power of true palm.
Infinite-level creatures, super-infinite-level beings, and the Aleph family, in the face of any true palm, will not be more powerful than any small carbon-based paramecium. They are all insignificant little ants.
In addition, like the previous luck master, the reason why he can 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, and therefore cannot exert his "universal ultimate".
the true power of reason.
But even so, Yun Zun can still easily display a powerful effect similar to Mu Cang's heaven-defying skill "I'll 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 endowment 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 powerful recording functions, 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 this "mysterious marrow" as the foundation core to reconstruct its 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.
By using this ability, Xuanzhang can perfectly display the essence of his own Xuanzhang (large cardinal numbers) in any universal mathematical universe or other types of mathematical realms governed by any background axiom system.
All power.
Generally speaking, 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 various mathematical structures, rules, logics and constructability standards; and all von Neumann's special expansion forms
The universe, which is deeply involved in the field of model theory and forcing logic, is a special complex universe; even a larger complex universe, and even a larger V-logic logical multiverse. Compared with any large cardinality, even with
Compared with the so-called 'minimum' big cardinal numbers - the world's cardinal numbers, they are so small and humble that they are almost as dust.
No, even dust is far inferior and 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 Way.
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 fake palms are such unlucky people.
For example, this is the case with Yun Zun.
According to the records in his memory, his original marrow was the logical configuration of "World Cardinality", which can be abbreviated as WC.
The basic definition of the so-called world cardinal number is:
If V_a is the model of ZFC, then a is a world base. (Satisfies Vk=|ZFC)
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 a low-level 2-WC (containing an unlimited number of WCs), nor is it a slightly higher-level 3-WC (containing an unlimited number of 2-WCs).
It is the k-WC world cardinality at the fixed point level.
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 k-WC 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 multiple "inside" it.
The so-called "unbounded" means that there is neither an upper bound nor a lower bound in 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... far beyond the reach of.
Let alone the high and unreachable base, even if the complete state of Yunzun possesses the world's base-level mysterious marrow components, how powerful it is, to be honest, Mu Cang can't even imagine it at the moment.
He could only roughly think that the entire mathematical universe he was currently in would be as small as an egg compared to the real Xuanzhang version of Yun Zun.
The enemy who caused the Master of Fortune to fall tragically from the Xuanzhang to the pseudo-master level and imprisoned him in a prison was none other than one of his unreachable cardinal-level kin - a man named "Pete Heavenly King"
Unknown Mysterious Palm.
Regarding the intelligence information about this mysterious palm, there was an inexplicable blank in Yun Zun's memory. There was no useful information at all. There were only large tracts filled with strong hatred, pain and humiliation. The torrent of emotions overflowed and washed away.
I don’t know what this King Peter did to actually make Yun Zun hate him so much, and it was so humiliating and painful.
Could it be that King Peter... also used similar ultimate insults or even more terrifying methods to 'entertain' Yun Zun.
Mu Cang has no way of knowing.
"so……"
Mu Cang said leisurely to himself, "I should try to rise to the level of true palm first, then find a true type territory with a large cardinality structural level to enter, and then imitate the large cardinality logical configuration contained in it through the endowment ability.
, complete the reshaping of the body, and then advance to the Mysterious Marrow Level True Palm."
Obviously, this is Mu Cang's next plan.
As for the enmity between Yun Zun and King Peter... what does that have to do with him? It's inexplicable.
In short, before the 'loophole portal' was completely constructed, Mu Cang immediately activated [Ling Yue Feifu].
Start trying and see if you can get back to the real palm level.
Activating effect——
(At this moment, I am the fake palm with all the talents incomplete≠The next moment, I am not the real palm with all the talents intact)
Buzz——
In an instant, Mu Cang's entire form and spirit suddenly became blurry and hazy, as if he was about to disappear into the countless universes.
After just a moment, his form and spirit suddenly stabilized, as if nothing had happened.
But only Mu Cang knew that he... succeeded, and successfully rose from the fake palm level to the real palm level.
At this moment, as long as He is willing, he can embed himself into the ZFC background axiom system of this true class territory, and then gain the highest dominance of the entire axiom system, and then redefine this von Neumann universe into another one.