Attributes skyrocket infinitely, I dominate the multiverse Chapter 689: Malo's Steps, indescrib

In fact, after obtaining all the memories of the governor of Zhenjie's chaos in the 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 the Zhenjie, Chaos Realm.

He has been stationed here since the birth of this vast community, and it has been countless 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 a tiny little 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. Hidden boundless dome.

This vast and extremely huge dome ring contains a total number of territorial communities of various sizes and structures, as many as mahlocardals, and the Floating Dream Community is just one of them.

As for the so-called Mallo cardinal numbers, also known as Machro 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 the Marlowe base is essentially a subtype of the unreachable base, or a super-enhanced version of the unreachable base.

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, it is expressed in detail that there is a large base k such that the set {λ \u003c k: λ} is an immobile set in k, and any unbounded closed subset of k intersects the aforementioned set, then k It's the Mallory 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\u003ck such that supaa?c, then c is not an unbounded closed subset of k, and vice versa.

Also, the mathematical definition of weak Marlowe bases requires that they 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 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 number itself, otherwise it will No more 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 be more detailed, any definable growth method, as long as it does not involve the existence of the Marlowe base number, then the existence of any unreachable base number you use will be unreachable by an unreachable base number under the Marlowe base number. 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 kind of cliff in the abyss with no roads or suspension 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, 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 weak Marlowe base, 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.

So just imagine, imagine there is an endless forest called [1 unreachable base], and there are endless trees of all kinds in this forest.

Then, if a 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. trees.

Then, 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, a high-dimensional structure forest, The forest of causal loops.

Anyway, as long as the [Big Forest] is [Unreachable Cardinal], it will definitely be completely included in this universe, and this universe--\u003e\u003e

...It is [Zhaoji].

So in a sense, the Marlowe cardinal number, which strengthens all limits to the level of stationary sets, is a further higher-order evolution of the concept of large cardinal numbers such as unreachable cardinal numbers.

By analogy, the relationship between the two is as if Xuanchengzi living in the three-dimensional world is life, and the chaotic world and floating dreams wandering in the abyss of loss 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 base numbers and unreachable base numbers is far greater than the above pair of examples.

Then, above 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 greatmahlo - the great Malo 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 base, there are overlapping and unbounded multi-level world bases. The structures of these levels are so complex that they are almost indescribable, and they are all larger than the so-called Cantor's absolute infinity. There are many huge ones.

Then there is the smallest unreachable base k0, and above it is the unreachable base 1.

As long as there is 1, there is 2. If k is the kth 1-unreachable base, then k can be called a 2-unreachable base, and below the 2-unreachable base, there are k 1-unreachable bases smaller than it.

By analogy, for each 3, 4, 5... below any n1 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, n's unreachable cardinality k is an unreachable cardinality for all ltn.

Then what is above these zero and zero unreachable bases is the super unreachable base, that is, k is the k unreachable base.

And above all these unreachable cardinal numbers is the field of Marlowe cardinal numbers.

For this field, if m is a Marlowe cardinal number, then all unreachable cardinal numbers under m are stationary sets in m.

To expand, it is a 2-unreachable base, 3-unreachable base of this structure that is formally presented as [k is the kth].

Reachable cardinals, 4 unreachable cardinals, etc., all the way to super unreachable cardinals, all belong to fixed point properties.

By analogy, we can get endless unreachable cardinal fixed points with increasingly higher levels of properties.

The stationary set means that for any fixed point with high-level properties, m is the mth cardinal number that satisfies this fixed point property.

In other words, the existence of m, the Marlowe cardinal number, is absolutely higher than the unreachable cardinal fixed points of any high-level properties.

After reaching this step, the field of Marlowe numbers has officially begun.

In fact, although all unreachable cardinal numbers will be trapped in resident sets, Marlowe cardinal numbers can use resident sets as bricks to carry out crazy stacking of themselves.

So on this basis, we can get 2 Marlowe base numbers, 3 Marlowe base numbers, 4 Marlowe base numbers...etc.

Then the Marlowe base number below 1 Marlowe base number will form a stationary set, the 1 Marlowe base number below 2 Marlowe base number will form a stationary set, the 2 Marlowe base number below 3 Marlowe base number will form a stationary set, and the 2 Marlowe base number below 4 Marlowe base number will form a stationary set. The 3 Mallo cardinal numbers will form a stationary set...and so on.

On top of this there is also the super Mallory number, that is, m is the m Mallory number.

But all of these are far smaller than the great Maloki number.

The higher-order large cardinal numbers that can completely surpass the great Marlowe cardinal numbers are the more profound and magnificent weakly compact cardinal numbers, and the other far more crazy large cardinal numbers above them.

It is conceivable how huge the [Yuanzhi Dome Ring Collection] must be, whose scale can be equated with the great Maloki number.

However, according to the intelligence information provided by Chaosjie Floating Dream Memory, even such a huge collection of dome rings is still an insignificant corner in the so-called [Yanyi Branch Defense Line].

Therefore, the vastness of that long and long line of defense is simply indescribable.

Note that this is not an adjective sentence, but a declarative sentence.

In the memory of Chaosjie Fumeng, the overall size of the Yanyi branch defense line is clearly the [indescribable base number].

This is a... far beyond unreachable cardinals, super-unreachable cardinals, Marlowe cardinal numbers, and super-Mallow cardinal numbers. At the same time, it is similar to the weakened form of the Susslin tree in model theory and topology - the Alonzayan tree. A mathematical concept closely related to higher-order large cardinal numbers.

The reason why it is indescribable is that the indescribable cardinality is so huge that even the first-order arithmetic theory that can only quantify objects cannot prove it, and cannot provide any effective description of it.

Only the more advanced second-order arithmetic theory that can quantify properties can fully present it.

In addition, weakly compact cardinals are also in the category of indescribable cardinalities.

But the difference is that if the indescribable cardinal is an endless and vast sea, then the overall area occupied by the weakly compact cardinal is just a wave.

And what scale will the other larger branch defense lines located above the indescribable cardinal level branch defense lines, and even those inevitable national main defense lines that surpass all branch defense lines, be like? Don't know either.

It can also be seen from this that in that huge and mysterious kingdom of necessity, unreachable cardinal-level mysterious palms like Chaos Realm Floating Meng and King Pit are probably just small figures.

"Hahaha, okay, okay, the bigger the better."

Mu Cang laughed heartily, "No matter--\u003e\u003e

No matter how big it is, it will only become a resource for my progress. "

While laughing, Mu Cang purged his powerful and unreachable base-level power that covered the entire floating dream community, the whole world, the whole world, and the whole universe, and suddenly got into the infinite number of the entire territory community. Every corner was buzzing and vibrating, and there were pieces of [Hollow Scars] that seemed to be crawling out of endless strange and strange objects.

Perhaps His power was too powerful and too barbaric, so for a moment the entire floating dream community linked by countless creation and destruction webways began to shake violently uncontrollably.

It seems like it will fall apart in the next moment and turn into a messy mess.

independent territory.

Facing the invasion of the undecided, if Huanjie Fumeng was still alive, he would definitely not be so rude and barbaric.

Because this can easily destroy the stability of the floating dream community, and then have a harmful impact on the larger Tianzang dome ring frame structure.

No matter how small the impact is, once it is discovered by the inspection department, it will be punished and punished.

Chaos World Floating Dream will only engage in a routine war with the incoming undecided forces step by step. When the war is over, both parties will pay the money and withdraw their troops and return home.

It seems a little difficult to deal with, but this is the normal situation in low-intensity war zones, and it has been like this for many years.

The floating dream in the chaotic world is a habit of fishing, and the forces of the undecided are basically destroyed, and there is even a tacit understanding between the two parties.

It's okay to fight casually, but what's the point of playing hard for your life?

But why does Mu Cang care so much about you?

With His nature, He has always done whatever He wants to do.

Especially after having such a first-class trouble-making skill as [Wujue Secret Strategy], Mu Cang has no scruples anymore.

So Mu Cang didn't care at all about the floating dream community that was about to collapse. He violently spread out his unreachable base level power, followed the countless empty scars, and soared towards the distant place that was preparing to attack here. The power of the undecided lies.

Mu Cang's violent behavior immediately caused tragic casualties to the undecided forces.

Countless undecided people who were several levels below the level of the untouchable void completely disappeared without even reacting.

Those high-level undecided people who truly stood on several levels of the untouchable void also disappeared in large numbers.

At the same time, Mu Cang also truly "saw" the strange scenery of the territory where the undecided were located through this active attack.

Free to read.