In fact, after obtaining all the memories of the governor of Zhenjie's troubled world.
Mu Cang had a deeper and more systematic understanding of this huge territorial community.
According to the information in his memory, the official name of this community is the Floating Dream Community.
That's right, this name is taken from the name of the governor of Zhenjie, Chaos Realm.
He has been stationed here since the birth of this vast community, and it has gone through countless cardinal years.
However, even though this territorial community is so vast, it can only be regarded as a small area among the various levels of national defense lines in the entire inevitable country, especially in the so-called [Yanyi Branch Defense Line].
It's just an extremely small corner.
The larger defense structure on top of this territory community, which has a super-finite number of various digital realms and uses the Grothendieck Universe where Mu Cang is located as the core, is called [Heaven.
The boundless dome of Tibet.
This vast and extremely huge dome ring contains a total number of territorial communities of various sizes and structures, as many as Mahlo cardinals, and the Floating Dream Community is just one of them.
As for the so-called Mallo cardinal numbers, also known as Machrot cardinal numbers, they belong to a type of large cardinal numbers that are so huge that they completely surpass the unreachable cardinal numbers and are closely related to the unreachable cardinal numbers.
Generally speaking, all Marlowe bases are unreachable bases, but not all unreachable bases are Marlowe bases.
The reason for this is that Marlowe bases are essentially a subclass of unreachable bases, or a super-enhanced version of unreachable bases.
For example, if a base is the smallest λ-th unreachable base, then it must not be a Marlowe base.
At the same time, if a base is a Marlowe base, then the sequence of the λ-th unreachable base in the set must be unbounded in the base.
As for the axiomatic structure of the Marlowe base number, to express it concretely, there is a large base k such that the set {λ It is the Maloki number.
Or it can be written as, if there is an unreachable cardinality a∈C for any unbounded closed subset C of k, then k can be called a Marlowe base number.
At the same time, if there exists a Also, the mathematical definition of Marlowe bases (weak) requires them to form a stationary set on the set of all regular bases under themselves. This is a mathematical property that is more powerful than simple inaccessibility.
.
And if they are required to form a stationary set on the set of all unreachable cardinal numbers under themselves, it is a strong Marlowe cardinal number.
At the same time, this also means that not only is the Marlowe base number itself unreachable, but the unreachable base numbers below it will also form an unbounded closed set below it.
In addition to this property, Marlowe numbers also have other special properties.
For example, if a cardinality is a Marlowe cardinality, then it must be its own unreachable cardinality.
The reason for this is that the unbounded closed set composed of unreachable bases below the Marlowe base must contain at least one unreachable base. At the same time, this unreachable base must not be the Marlowe base itself, otherwise it will
It's no longer boundless.
Put aside these boring mathematical theories, in short, you only need to know that no matter how hard you try, the unreachable cardinal number can never exceed the Marlowe cardinal number.
Or to put it in more detail, any definable growth method, as long as it does not involve the existence of Marlowe base numbers, then the existence of any unreachable base number you use will be eliminated by an unreachable base number under Marlowe base numbers.
The base is completely capped.
The reason why this happens is that all unreachable cardinal numbers that are completely smaller than the Marlowe cardinal number will form a "stationary set".
And [Zhuji] is like a cliff in the abyss with no roads and no ropes, firmly trapping all inaccessible bases from top to bottom.
As for the so-called resident set, in logic, especially in the set theory system, it refers to a set that is related to a certain type of operation or structure on it.
For example, in the field of Marlowe cardinal numbers, a stationary set refers to a set of cardinal numbers, which contains all unreachable cardinal numbers, and each unreachable cardinal number is one of the elements of the stationary set.
If expressed in mathematical language, that is... If k is called a Marlowe base (weak), then all regular bases in k will form a stationary set of k.
At the same time, if all unbounded closed subsets of S and k intersect and are not empty, then S?k is the stationary set of k.
To be honest, all these explanations, either directly explanatory or almost purely mathematical, seem a bit mysterious and confusing, making people confused.
So just imagine it, imagine that there is an endless forest called [1-unreachable cardinality], and there are endless trees of all kinds in this forest.
Then, if a certain being sets out from any tree in this large forest that is essentially a certain type of unreachable cardinal number, then no matter how many steps he takes and how many lifetimes he takes, he will never be able to reach any other tree.
of trees.
Next, imagine that there is a boundless multi-dimensional universe. This vast universe contains all ‘things’ with the attribute of [big forest].
Whether it is a carbon-based wood forest, a silicon-based crystal forest, a sulfur-based flame forest, a mystical flesh and blood forest, a polar ice forest, a desert gravel forest, an ancient and modern time forest, or a high-dimensional structure forest,
The forest of causal loops.
Anyway, as long as the [Big Forest] is an [Unreachable Cardinal], it will definitely be completely included in this universe, and this universe... is the [Resident Set].
Therefore, in a sense, the Marlowe base number, which strengthens all limits to the level of stationary sets, is a further higher-order evolution of the concept of large base numbers such as unreachable base numbers.
This chapter is not finished yet, please click on the next page to continue reading the exciting content! By analogy, the relationship between the two is as if Xuanchengzi living in the three-dimensional world is life, wandering in the chaotic world floating in the abyss of loss.
Dreams are also life.
At first glance, the two seem to belong to the same category, both beings, but in fact they are very different and cannot be compared at all.
The gap and difference between the real Marlowe bases and unreachable bases is far greater than the above pair of examples.
Then, on top of this Tianzang dome ring is a so-called dome ring set named [Yuanzhi].
As the name suggests, a dome ring set is a higher-order territorial aggregation structure that contains a certain type of unbounded dome rings with an unknown large cardinality.
Mu Cang learned from the memory of floating dreams in the chaotic world that this so-called "certain unknown large cardinal number" actually refers to the Greatly Mahlo - the great Mahlo cardinal number.
If you want to fully understand the great Maloki numbers, you need to go through an extremely long journey.
The first thing you need to know is that under the smallest unreachable cardinal number, there are overlapping and unbounded multi-level world cardinal numbers. The structures of these levels are so complex that they are almost indescribable. They are all larger than the so-called Cantor's absolutely infinite size.
Lots and lots of greatness.
Then there is the smallest unreachable base k0, and above it is 1-unreachable base.
If k is the kth 1-unreachable base, then k can be called a 2-unreachable base. Under the 2-unreachable base, there are k 1- unreachable bases smaller than it.
Unreachable base.
By analogy, for each 3-, 4-, 5-... below any (n 1)-unreachable base k where n is the subsequent ordinal number, there are k n-unreachable bases smaller than it.
When n is the limit ordinal, the n-unreachable base k is for all m
