Into the Immortal Cultivation

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In the three years of Uli, Lizong and Lianzong very rarely reached a new consensus.

If a formula has exactly the same implication in the detached and successive calculus, then, it can be said that this formula is "absolute".

This "absoluteness" undoubtedly gives Lizong some kind of "hope".

For them, this is simply the last salvation and the only gospel that can be found under a ruthless blow.

The existence of "absoluteness" may indicate that mathematical entities are ubiquitous in different mathematical axiom systems.

If this is the case, the mathematical entity itself may have the "actual completion" nature.

This is their last hope.

Perhaps they need to find a new way to explore the nature of this mathematical entity.

At this point, the purpose of Feng Luoyi and Geting School is surprisingly consistent.

They even put down some differences for the time being and explore this area together.

In this process, Hai Ting real people finally emerged.

Since Lian Zong proved that the logic of intuitionism is not safer than the classic logic of the Gotting School, he seems to be a person, silent and speechless.

In Li Jing's initiative, his tendency to autism was even more serious.

However, this does not prevent him from continuing to shine as a mathematician.

He was inspired by Su Junyu's continuum research, introduced Feng Luoyi's research on good foundation collection in the infinite axiom, and created a new school-constructivism.

Within a certain theory, it is a constructable class to traverse "ordinal numbers of all ordinal numbers" with a finite number of symbols and all entities defined until the height of the reflected sequence.

The constructable axiom is to declare that the population formed by the legal set under the good basis sequence is equal to the "constructible set".

He inherited the idea of ​​"Study of mathematics is a product of construction", but it accommodated the set theory that he hated, and completed the preliminary security proof on the basis of Feng Luoyi's set.

Definition is construction, construction is proof, and proof is rank.

It is precisely because of this that he also made a small breakthrough in the theory of calculators and entered the vision of Qianji Pavilion.

The Gotting School was a little alarmed.

The existence of Feng Luoyi and Turing [maybe even counted as Wang Qi] made the Qianji Pavilion, a branch of the Ten Thousand Famen, always the back garden of the sect.

There have also been monks of Lianzong, and even the head of Lianzong, such as Shujun, developed a parallel arithmetic theory.

However, Hai Ting was officially entered.

He even has a tendency to show favor to Lizong. Hai Ting real person even proved that the key difference between intuitionism and other logic schools lies in "whether you can manipulate infinite or even ultra-poor entities with a finite number of symbols".

But the appearance of Hai Ting's real person is not entirely a bad thing for the Geting School.

At the same time as the rise of Hai Ting, he also proposed a lot of things corresponding to the theory of Lizong's past, which enabled the Gotting School to reflect on itself and discover many things that may not be found in the past.

They found that many of the same mathematical structures existed widely in different axiom systems. The choice of axiom system only affects the number of mathematical structures that can be proven.

The selection and analysis of axioms is actually to determine which basic principles are used as the "starting point" and "benchmark" of mathematics.

The existence of numerous axioms was not established on the basis of judgments on the basis of mathematics, but the establishment of these axioms by the research activities of the monks of Falun Dafa [such as the definition of addition and the definition of subtraction].

These have further strengthened Lizong's confidence in "calculating entities".

It is against this background that Su Junyu, through the idea of ​​Hai Ting's real person, proposed a sao operation called the "transfer model".

If there is a mathematical axiom system A, which has its own consistency, then there is a model of this system.

Adding the axiom "System A is consistent" to the original system, you get "System A is the system after adding System A consistently." Then, there is "System A is consistent. The system after joining System A is consistent." Then add "System A is the same system after joining System A", and add "System A is the system after joining System A" ... so repeatedly, until infinity.

Then, the "consistency" of System A will be transferred to "infinity" itself, becoming a "countable infinity" nature.

This made Su Junyu greatly improved, and even almost reached the virtual refining period.

Now he, instead, like Wang Qi, suppressed his own cultivation behavior to adjust his power.

Under the idea of ​​the transfer model, the "constructive model" is once again mythical.

Constructable operations are "absolute" for any transfer model of arithmetic axioms.

Very rare things happened.

Under the joint efforts of Lianzong and Lizong, an arithmetic result established within both Lizong and Lianzong was established.

Therefore, at this time, Hai Ting's infamous "Lianzong traitor" infamy even exceeded the sum of "Lizong traitor" received by Chen Youjia, Feng Luoyi, and Wang Qi.

Even Hai Ting, the real person, had to cross the fairy road again and chose to avoid the disaster temporarily.

However, he didn't care about this anymore.

He was invincible again.

Like the infinite axiom proved by Feng Luoyi, under the good basis set, the complete set is equal to the proposition of constructable class, which is unprovable.

He has become invincible.

Constructivism is already invincible.

Even if Shujun could slap him to death, this result could not be changed.

For this, Feng Luoyi was not happy.

He sighed: "When I first agreed to the Court of Justice, I just thought that to correct the name of the infinite axiom and the law of exclusion, and to correct the name of the departed, can also be regarded as offsetting ... the disastrous consequences of Wang Qi's inaccurate calculation. I really did n’t expect that things would look like this. "

Wanfamen is completely crazy.

Both Lizong and Lianzong have shown a tendency to "disregard everything." They no longer care about what they will do in the future, they just want to do their utmost to kill their opponents in this mud — even if they themselves are also stuck in the mud.

Not only between Lizong and Lienzong, Lizong to Lizong, Lianzong to Lienzong, they are also tolerant.

Hai Ting real person is an example. He clearly has some responders, but he can only withdraw from this sphere of influence.

And Feng Luoyi also felt a little malicious.

Instead, Su Junyu is still responding to the song court.

But Feng Luoyi knew that the man with the surname Fan was even trying to "point" Su Junyu.

He has detected two or three such malicious "points".

However, that bastard's **** has never been a mere conspiracy.

I'm afraid he can see what happened?

Even though Chen Youjia and Su Junyu both showed a different tendency from Wang Qi, but they have communicated with Wang Qi for a long time, and their fundamental views on arithmetic are always consistent with Wang Qi.

They have exactly the same "ultimate goal", looking forward to the same picture.

Mathematics is self-contained and will not be shifted by human will.

Therefore, what Van Bach knows will not be changed by the will of Su Junyu or Chen Youjia.

This is really scary.

Real Turing also shook his head: "In this case ... the one who looks forward is also carried an unknown prophecy ..."

Lizong and Lianzong, Geting and Shaoli, the two sides are begging each other. Despite the achievements of each other, they also dismantled each other's many achievements.

While making great progress, both sides were hurt.

Under such circumstances, Wang Qi, who is in a foreign country and devotes himself to compiling the original plan, has become the "Star of Hope" that is not much left in the Ten Thousand Fas.

But unfortunately ... ten years, no, no, less than seven years, this "Star of Hope" is also at risk of falling.

Many people feel that Wang Qi's arithmetic may also have huge loopholes.

-This is simply the tone of Wanfamen's self-extinguishment.

This desperate thought has appeared more than once.

Feng Luoyi didn't say anything.

In the winter of this year, the Gotting School was not very happy to declare that it seemed that it had completed further proof of the first question of Ximen's twenty-three questions.

Deeper than Su Junyu's.

They proposed the concept of "inner model".

Any transfer model that contains "ordinal numbers of all ordinal numbers" is an "inner model".

Constructable class is the smallest internal model.

Within the constructable class, the cardinality of the infinite set must be in the form of several powers of two. Therefore, the generalized continuum hypothesis holds.

Any equivalent or reduced form of the generalized continuum hypothesis cannot be proved.

After borrowing the definition of Xinlianzong, they finally went one step further.

This scene is really awkward, so that the cheers inside the court are all sparse.

They also completed the exploration of choice axiom.

At this time, one person showed obvious dissatisfaction.

Su Junyu sighed: "The continuum ... its follow-up should not be like this."

The preliminary proof of the continuum hypothesis was completed by him. He also has feelings for this issue.

For him, the inner model really violated intuitive feelings and violated the "aesthetics" he had as a monk.

how to say……

It's uncomfortable.

"Circulation is the most constant phenomenon in the universe. Deleting the cycle in arithmetic and refusing to model it is simply ..."

He shook his head. Wang Qi is now his boss, and Feng Luoyi is Master Wang Qi. But he still doesn't like the concept of Liangji collection ... well, I'm afraid Wang Qi won't like it too much?

On the other hand, Hai Ting is also true.

It is too optimistic to think that there is only "constructible sets" in the totality of set theory.

In the final analysis, the entire "inner model" was developed on the basis of "relative consistency".

Relative consistency has the meaning of "compromise for perfection" itself.

Consistency is achieved by discarding those that cannot coexist.

Cut your feet to fit your feet, cut your toes to avoid insects.

He wanted something stronger ...

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