The Shuluo realm where the other party was born actually had a master.
All rules and events, all logic and boundaries are under the full control of the world's cardinal level master.
But Peter's [Domination Invasion] is really too outrageous.
So when the one in charge became aware of Peter's existence, and unfortunately wanted to observe him, everything was irreversible.
In just an instant, the person in charge became Peter's "captive" and became his miserable son.
And that time, which led to the complete change of ownership of the territory, Peter suddenly learned about it.
It turns out that beyond everything he knows, there is a wider and more wonderful world.
Thus, a Pit Heavenly King who feeds on those who hold the Way and those who are undecided... was born.
From then on, no matter which digital realm or weird realm, whichever leader or undecided one, they all became the prey of King Peter.
Ever since he stepped out of his "hometown", King Peter has unscrupulously taken possession of all the people, objects, and territories he met.
No one has the power or qualifications to stop Him even half a step.
Even King Peter eventually became a third-party force independent of the Kingdom of Necessity and the Kingdom of Freedom.
He is extremely feared by both the Taoist clan and the Undecided clan.
In a sense, King Peter has ushered in an era that belongs exclusively to him.
However, after traveling across all realms of the Lost Abyss for endless years, King Peter's journey of willfulness was eventually ruthlessly interrupted.
That was, a long, long time ago.
During those years, King Peter had clearly discovered the upper limit of strength in the entire "world", or in other words, the level of the strongest people of the two races.
That is, the Icarus cardinal series.
As for the higher levels, King Peter knows from the information he has collected that such powerful people may only exist in the meaningless source and on the omniscient tower.
In other words, there may be Mysterious Palms on the Omniscient Tower that completely surpass and surpass the Icarus Cardinal Level of the Reinhardt Cardinal Level, or even higher-level Great Cardinal Levels.
Therefore, in that ancient era, King Peter, who had advanced all his masters and undecided clones to the Icarus base level and the [perfection number] level, and felt that he was an invincible master and lonely, then
With great arrogance, he broke through the many high-level defense lines and headed towards the omniscient tower in the core area of the inevitable country.
Then... there is no more.
King Peter now only vaguely remembers that when he led the army of clones composed of Icarus bases and stepped into the bottom base area of the omniscient tower... he knew nothing.
When he woke up again, he could only find some unknown and unfamiliar conceptual information in his extremely vague memory, such as "Supreme Eye", "Transcendence Selection", "Above the Mysterious Palm"... and so on.
At the same time, King Peter also discovered that most of his clones had perished.
The few remaining clones also fell from the Icarus base level, to the world base, unreachable base, Marlowe base... and other "low" levels.
And what's even more outrageous is that King Peter discovered that his [Domination Invasion] ability was also affected by an unknown factor.
Both the target and the number of bodies seized are inexplicably blocked within the super huge base field, and there is no possibility of unblocking them.
Regarding this point, in the years that followed, King Peter conducted various tests using clones of various levels.
But, they all failed.
Whether facing the mysterious palm of the Icarus base level, or the top undecided person of the [Ultimate level], his clones are unable to carry out any body snatching, and can only be ravaged and killed by the opponent.
In the end, King Peter could not gain anything except the destruction of some clones in vain.
At the same time, King Peter also discovered a situation that shocked him deeply.
That is to say, all the "traces" left by Him inside and outside the entire kingdom of necessity and freedom have become blurred and even beyond recognition.
The many masters and undecided people who originally knew more or less information about King Peter, actually all forgot about his existence.
The main defense lines, branch defense lines, dome ring collections, boundless dome rings, territorial communities, etc. at all levels that were dilapidated, collapsed, disintegrated or even destroyed because of King Peter, were all distorted and mutated.
Either from a huge main defense structure to a smaller unbounded dome ring, or from a collection of dome rings in a necessary country to a grotesque territory in a free country, or from returning to the end that has long been destroyed, or even from the end at all.
The unborn appeared.
In short, it is as if King Peter has never existed before, and all the changes related to him have turned into vague and specious rumors.
Faced with this extremely weird situation, King Peter was completely frightened.
He knew that he must have offended some unknown supreme being, which led to this horrific result.
And that supreme being most likely exists on the tower of omniscience.
So since then, King Peter has changed his original extremely arrogant and domineering style, and has become much more low-key and secretive.
Although I don’t know why the Supreme Being didn’t take my own life, He, who was timid and afraid of death, still hid for a long time before daring to show up.
And after showing up, he didn't dare to seize the body at will, let alone occupy the territory and become the king at will. He only dared to secretly disperse all the clones in countless territories.
However, although he lost the courage to continue to do things, driven by curiosity, King Peter still secretly began to investigate the "Supreme Eye", "Transcendence Selection", "Mysterious" in the long years that followed.
"On the palm of your hand"...etc. information on vocabulary concepts.
This chapter is not finished yet, please click on the next page to continue reading the exciting content! Perhaps because he is patient and persistent enough, King Peter really found out a thing or two about these unfamiliar words.
The first is the "Supreme Eye", which can be known based on the information it has spent time and effort gathering from various places in the Kingdom of Inevitability and the Kingdom of Freedom.
The so-called "Supreme Eye" is an unconfirmed and mysterious legend with a long history.
Legend has it... that the entire "world" where all the masters and undecided ones live are born from the "Supreme Eye".
At the same time, after the birth of the "world", the [meaningless source] was born from the "Supreme Eye", and finally the undecided family and the free country emerged.
"Crossover Choice" and "Above the Mysterious Palm", after the exploration and research of Peter King, it was finally discovered that there is a profound connection between the two vocabulary concepts. They are also two concepts that are spread in various fields.
Mysterious rumors.
The former, the so-called "overpass selection", actually refers to... if you can jump over or bypass the axiom of choice, you can reach a new field.
What the latter refers to is exactly that new realm - above the Mysterious Palm.
Yes, Xuanzhang is not the end of the Taoist's evolutionary system.
Above it, there may be a grand and majestic new realm.
As for the content of the axiom of choice (given a series of sets, one element can be selected from each set), it is an important part of the ZFC axiom system.
Without it, the measure theory of real numbers will fall apart, and there will be a series of mathematical structures of uncountable infinity and above, that is, all kinds of zero and zero large cardinal numbers and high-order large cardinal numbers, and various large and small occurrences will also occur.
changes.
In short, through the collection of a large amount of information and careful research, King Peter finally concluded.
If you want to truly and safely set foot on the omniscient tower, even if you just climb to the base area at the bottom of the tower.
It is very likely that the life and strength levels of climbers are required to reach the level corresponding to the large base after completely overcoming the axiom of choice and entering a new field.
That is, the Reinhardt cardinal number, and the higher-order large cardinal numbers above it.
That's right, it's that big cardinal number that's always entangled with the concept of "0=1".
And the reason why it always has the name "0=1" is closely related to the axiom of choice.
In other words, it is because of the contradiction and incompatibility with the axiom of choice that the Reinhart cardinality is labeled "0=1".
The so-called Reinhart cardinality is an important mathematical concept in set theory.
Its definition and structure can be elaborated from many aspects.
First of all, the definition of Reinhardt cardinality is a special type of cardinality that exists under the set theory system ZF axiom system without the Axiom of Choice (AC).
Expressed in mathematical language, there is a non-trivial elementary embedding j: V→V, crt(j)=k, and this k is the Reinhart base number.
So specifically, it refers to the critical point crt(j)=k of this non-trivial basic embedding.
The embedding j is elementary, which means that all true propositions that are true before embedding will still be true after embedding.
The other V refers to the universal von Neumann universe of set theory, that is, the true type of all sets.
Therefore, if we combine these and elaborate further, Reinhardt cardinality involves a non-trivial basic embedding, which maps the entire class V of set theory to itself and has specific critical points.
Among them, there is also a characteristic of Reinhardt base numbers - self-embedding, elementary embedding from itself to itself.
The so-called "non-trivial embedding" in the previous paragraph refers to the Reinhart cardinality itself, which is actually the critical point of the basic embedding.
As for the expression of this critical point in mathematical language, it is...k is the critical point of embedded j, that is, for all ordinal numbers a less than k, j(a)=a, but j(k)≠k.
Then, this embedding will map the entire class V of set theory to itself, and it is not an identity mapping - that is, there is a set x such that j(x)≠x.
At the same time, since embedding j has a critical point k, this means that for all ordinal numbers a less than k, there will be j(a)=a, and for k itself, there will be j(k)>k.
To put it more specifically, this embedding will have specific properties, which will map certain elements in V to other elements in V, and some structures or properties of the set will remain unchanged during the mapping process.
Secondly, because it cannot be described or defined by first-order logic language, Reinhardt cardinal numbers are also undefinable.
Also, in addition to these, what really causes the Reinhardt base number to have the title property of "0=1" is the inconsistency between it and the standard set theory axiom system ZFC with the axiom of choice.
sex.
It can also be called, the library energy inconsistency theorem.
The content of this theorem is that in the set theory system with the axiom of choice, there is no non-trivial basic embedding that can map the entire class V to itself.
To put it more specifically, within the overall framework of the ZFC system, there is no cardinality that can satisfy the definition of Reinhardt cardinality. It must be established in a set theory system without an axiom of choice (such as the ZF system).
and discussion.
The reason for this is that the definition of Reinhardt cardinality involves non-trivial basic embeddings.
According to the library energy inconsistency theorem, this kind of embedding cannot be established in the ZFC axiom system at all, or it will lead to serious inconsistencies, which will lead to various conclusions that are contradictory to known mathematical facts.
In addition to this theorem, there are other mathematical results and reasoning that show that Reinhardt's cardinality and the axiom of choice cannot coexist logically. These counterexamples further support the incompatibility between the two.
Therefore, in a self-contradictory axiom system (Reinhardt cardinal number ZFC), naturally any messy proposition can be given a truth-forcing proof.
For example...0=1.
Therefore, the Reinhardt cardinality has no choice but to have the so-called "0=1" label.
In fact, it is not only the Reinhardt base number that is inconsistent with the axiom of choice and the ZFC axiom system.
The same is true for the Berkeley bases with greater consistency strength, super Reinhardt bases, unbounded closed Berkeley bases, and even larger and more distant known and unknown large bases.
The further essential reason why such contradictions arise is because the addition of the axiom of choice provides set theory with too many degrees of "choice" freedom.
For this problem, either accept the ZF axiom of the existence of Reinhardt cardinal numbers and do not choose the axiom; or accept the ZF axiom of selection and do not want the axiom of the existence of Reinhardt cardinal numbers; or... build an axiom system more powerful than ZFC.
This expanded and upgraded higher-order axiom system may include some additional axioms that allow the existence of Reinhardt bases, and then allow the establishment and existence of Reinhardt bases and more powerful bases above it.
"So the so-called omniscient tower..."
Mu Cang, who had exhausted all the memories of King Peter, slowly turned his head and "looked" at the empty abyss of loss, as if he was "looking" at the omniscient tower that did not know where it was located, and said quietly:
"Could it be a higher-order axiom system... that can accommodate the existence of Reinhardt's cardinal logic configuration?"
