When the infinite mathematicians from various intelligent civilizations in the infinite universe throughout the ages deduced and demonstrated the ultimate mathematical concept, they were faced with another problem that needed to be solved urgently.
That is, how to give an appropriate name to this ultimate concept that seems to be the core foundation of the entire mathematical system?
What is quite strange is that after this idea came up, the endless mathematicians in the infinite time and space inexplicably and unanimously in their hearts... flashed a name out of thin air - [Mu Cang].
The name came very naturally, almost like breathing.
Therefore, countless mathematicians naturally used the language of their own civilization to name the ultimate concept that supports various axioms of the entire mathematical system... "Mu Cang's Axiom".
And now, the true ontology or origin of this ‘ultimate axiom’.
Mu Cang, the Almighty God at the world cardinal level who stands at the pinnacle of the mathematical axiom system of Gödel's constructable universe, is reading through the huge memory information of the three mysterious palms.
In fact, Mu Cang has never experienced the so-called configuration imitation and mystical marrow transformation in the whole process, let alone any ontological reconstruction and transformation and sublimation.
Under the mysterious power of the heaven-defying magical skill [Infinite Secret Strategy], he directly skipped all the processes and procedures, and was promoted to a large-base life form - a mysterious marrow-level Taoist master in one step.
Although the Mysterious Essence Core that Mu Cang possesses now is only the smallest large cardinal number - the axiom logical configuration of the world cardinal number.
But a big cardinality is a big cardinality.
Even if it is just the world's cardinal number, it cannot be compared with any existence below the level of a large cardinal number. There is no comparability at all.
In fact, the imagination of intellectual life is extremely poor.
It is so poor that it is impossible to use any visual words to describe the smallest large cardinal numbers such as the world's cardinal numbers. It can only be described in an extremely vague way through sideways generalizations mixed with mathematical language.
So, how should we describe or express the hugeness of the world’s base?
Let’s start from the beginning.
From a set theory perspective, infinity is a limit rather than a specific numerical value.
Therefore, what is always compared between infinities of different series is the size of the so-called "potential".
For example, through the infinity axiom, all natural numbers are defined as level 0 infinity (n), then based on this, all subset numbers of level 0 infinity can be defined as higher level 1 through the power set axiom.
Infinity (2^n).
Therefore, by analogy, we can construct a series of infinities of level 2, infinity of level 10, infinity of level 100, and so on... until the infinity of level infinity.
The size of these various series of infinities compared with each other is also the size of "potential".
Then we can also let the infinite level infinity be k, and then on this basis we can construct higher k level infinity, k level infinity level infinity, k level infinity level...(k infinity levels)...infinity and so on.
After going through countless endless loops over and over again, through the function and the △ formula, the fixed point can be obtained.
On top of it, there are still more and larger fixed points, as well as endless PA fixed points, and infinite PA fixed points.
Then, at the top and pinnacle of a series of fixed points that are so numerous that they cannot be described with infinite and countless endless means, there are the so-called supreme heaven, the supreme kingdom of God, and the final shore... all kinds of
The Σ2-world cardinal number is far beyond description by adjectives.
Note that it is Σ2-world cardinality, not world cardinality. The two are two completely different concepts.
For the Σ1-world cardinality, if a is a power-allowed cardinality, then Va is a model of ZFC-.
〖ZFC-〗 means that the substitution axiom of ZFC is completely limited to the scope of the Σ1 formula.
As for the Σ1 formula, it is a first-order existential proposition with only one unbounded existential quantifier at the beginning.
The so-called "unbounded" means that it will be larger than any given bounded value. If you want to reach the Σ1-world cardinal number, you need to close all recursive operations of the Aleph function.
As for the Σ2-world cardinal number above this, it is much more complicated and huge, because the beginning of its mathematical formula is an unbounded existence proposition and is linked to an unbounded universal proposition.
From the perspective of set theory, that is, if a is a Σ2-world cardinal number, then as long as a has certain local properties, there must be unbounded many k
