Enter the Immortal Cultivation

What Wang Qi wanted to tell Feng Luoyi was naturally the internal model plan.

The relationship between the internal model and the constructible class is almost the same as that between flowers and fruits. The constructible class is the flower, and the internal model is the fruit.

However, the internal model has fatal flaws after all.

First of all, it is completely based on well-based sets. And there are indeed parts of mathematics that can only be mastered by non-well-based sets.

Moreover, it also excludes cycles and does not contain infinite descending chains.

In addition, it cannot accommodate large cardinal numbers including the first and second unreachable cardinal numbers.

There are many benefits to large cardinal numbers. As mentioned before, the introduction of large cardinal numbers can directly prove that any constructible real number set will not cause the ball-dividing paradox, and there is no need to cancel the selection function; the introduction of large cardinal numbers can prove the completeness of second-order arithmetic, and so on.

And if the theoretical system of the foundation-building school wants to develop, it must have a large cardinality.

But the internal model is not completely useless.

The continuum problem can actually be regarded as a third-order problem. And large cardinal numbers just can't solve third-order problems.

The inner model can solve the problem perfectly.

Therefore, abandoning the inner model for a large cardinality is a foolish thing to do.

Therefore, Wang Qi came up with an idea.

A very natural idea of ​​"putting them together to make peeing beef balls".

Starting from the inner model, using the forcing method, continuously adding elements, and expanding the mathematical model itself step by step until it can accommodate a large cardinality.

The forcing method itself is to expose the connection between two different sets by continuously adding elements, and finally achieve an effect of "letting the theory prove itself".

The inner model plan is the ultimate calculation of the meta-calculation.

Wang Qi said it easily, but Feng Luoyi was shocked.

"This... do you know what you are talking about?" He paced back and forth in the room.

In fact, when the foundation-building program appeared, his attitude towards the good foundation set was somewhat shaken.

Van Bach has already pointed out that the good foundation set is not enough to accommodate the calculation of the foundation-building school.

The inner model is also built on the good foundation set.

If his theory must exclude such a great thing...

In front of the foundation-building program, he did waver in his belief in his own achievements.

That is, this part of the things has just been made and has not been incorporated into the body, so he can act so relaxed.

But Wang Qi's words rekindled his confidence in his achievements.

Perhaps, he is not the one who is ultimately right. But after all, he is the one who has paved the way for mathematics.

Feng Luoyi took a deep breath and said, "If I tell those people in the Goting School, they must be crazy."

At this point, Feng Luoyi couldn't help but confirm again: "Do you really know what you are talking about?"

Wang Qi nodded: "I know, I know, I understand."

The internal model plan can also be said to be an upgraded version of another Hilbert plan, which is a big plan.

In addition, this is also the last banner of the new formalists.

Or, this is to extend the life of the Goting School.

If there is no such plan, then the Goting School will not have any direction to participate in pure mathematical research in the foreseeable future.

With this, it can support for a few more days.

It is impossible to surpass the Foundation Building School. The Foundation Building Program and the Basic Lemma have already destined the Foundation Building School to have the future.

In the future of Wanfamen, every mathematician will use the ideas, naming, and methods of the Foundation School.

But at least the decline can be slowed down.

Before the Foundation Building School reaches the top, Wang Qi still needs to worry about whether the extension of the life of the Ge Ting School will affect the development of the Foundation School.

But now, there is nothing to worry about.

Unless the Master of Calculation suddenly changes his nature, his interest in pure mathematical principles suddenly exceeds the application, and he also presides over the Shao Li School wholeheartedly, it is possible to slightly delay the rise of the Foundation Building School.

But for many years, no one will be able to surpass the Foundation School in "stealing disciples".

"You...you..."

Feng Luoyi wanted to say something.

But Wang Qi said: "Even if set theory is no longer the foundation of mathematics, the calculation of the original calculation has a strong guiding significance. This itself is also of great benefit to the Foundation Building School."

Feng Luoyi knew that this was the truth.

The theoretical system of the foundation-building school must have the concept of "large cardinality".

Incorporating large cardinality into the inner model is a supplement to the theory of the foundation school.

In fact, the inner model plan itself is parallel to the Bourbaki school and the Langlands program, but it has a positive impact on the latter two.

This is of great benefit to the foundation-building school.

What's more, what Wang Qi needs to worry about now is no longer whether the foundation school can rise.

He is more worried about whether the foundation-building school can go on for a long time.

The old predecessors in Shenzhou can live forever.

Wang Qi plans to take advantage of this point.

The foundation-building school does need the top position of the Wanfamen.

However, without opponents who covet this position, the foundation-building school may not last long.

Other schools will always burst out new vitality through "accidental discoveries".

But the Bourbaki school itself has no "accidental discoveries". For them, only what is in the textbook is mathematics.

If there are other scholars who follow different ideas and continue to provide such "accidental discoveries", and then the foundation-building school constantly incorporates the new things into its own system, that would be almost the ideal model.

Wang Qi felt that Suan Jun might still have potential and continue to fight for the growth of the foundation-building school for a hundred years... I mean, to be an enemy for a hundred years.

But there can't be only one Suan Jun.

The Snow Country School took the initiative to show goodwill, most of them are friendly forces, Hai Ting Zhenren is weak and has a shallow foundation, and Turing Zhenren is a partner that he must have to upgrade his skills in the future, so it's too late to cooperate.

After thinking about it, the Ge Ting School, which has deep roots, is the most suitable.

Extending the life of the Ge Ting School is also part of Wang Qi's plan.

Feng Luoyi finally just looked at Wang Qi deeply and then went out.

That day, Feng Luoyi did not come back.

Wang Qi did not treat himself as an outsider. He made tea and took snacks by himself, thinking and waiting.

The next day, the Huanliu Fairy Ai Ruoche rushed over.

She said to Wang Qi: "I will never forget your kindness."

The Master of Calculation had already left Shenzhou, and He Waier was a Lianzong monk. So at this time, she came on behalf of Ge Ting.

Wang Qi smiled: "Helping you is helping myself. The Ji faction really needs this plan..."

Ai Ruoche said: "That's different. In short, you really helped me in times of need this time. In our hearts, you will always be a member of Ge Ting..."

Speaking of this, Ai Ruoche was a little embarrassed: "You are also a leader of a faction now. With your status, it is really inappropriate to say this to you. But, what we mean is... If you ask again, we will go through fire and water without hesitation."

"Going through fire and water is too exaggerated." Wang Qi waved his hand: "There is no need to give in on academic issues, otherwise, it will seem that I am taking advantage of the favor. If there are other problems, I will definitely ask Ge Ting."

Just kidding, he is now asking for the "Raising Wolves Plan". If the whole world has a positive reputation, and then everyone works together to build the foundation outline, and the members of the foundation school lose interest in their own school in a few years, then he has worked in vain!

—— How fresh, Wang Qi, who has a high negative reputation, actually worries that his positive reputation is too high one day!

Ai Ruoche naturally nodded.

But soon, Wang Qi received a lot of invitations to preach.

Among them, two are the most outstanding.

One is from Gatingzhai, and the other is from Huabotang.

They are the holy places of Lizong and Lianzong in the past.

"What the hell, it's still too high." Wang Qi thought so and accepted the two.

Are you kidding me? When will there be an opportunity to preach in the holy places of Lizong and Lianzong?

Even he can't rely on such invitations to come every day.

And this is to go to two at a time.

In the next month, Wang Qi gave several more sermons in succession.

First, Gatingzhai and Huabotang.

Then there were a few for students of the academy, and a few for ordinary cultivators.

Because of his previous speech, the theory of the foundation-building school has become a symbol, representing the process of mutual understanding between humans and aliens through rationality.

Against the backdrop of the gradual migration of humans to other places, the effect of this speech is undoubtedly amazing.

Wang Qi once thought that the foreign land was a perfect place to start.

However, he really did not expect that the effect would be so good.

Overnight, Wang Qi went from being known only by the Wanfamen, and others only knew that he was a genius, to a star scholar.

His name spread throughout the streets overnight.

Ordinary people may not understand pure mathematics or foundation-building guidelines.

But they know about the foreign land, and they can see that going to the foreign land is an opportunity to easily realize the dream of rapid success.

And the appearance of the alien race makes them think about it.

The teaching aids that Wang Qi used for the lecture that day - those regular polyhedrons shaped like dice, engraved with the same sentence written in different languages, were quickly copied and became the most fashionable decorations.

Businessmen with business acumen called it "Wangqi Polyhedron".

Then it was sold out instantly.

Even monks felt that it was quite impressive to be able to visit a "Wangqi Polyhedron" at home.

Because "Wangqi Polyhedron" is the manifestation of the foundation-building outline, a mathematical achievement, in the field of aesthetics.

Wang Qi himself did not expect that there would be such a trend.

After Wang Qi knew about the "Wangqi Polyhedron", he said to Chen Youjia with a smile: "Giving gifts will be really simple in the future. Wang Qi carved the Wangqi Polyhedron himself, how impressive it is to say it out!"

Chen Youjia glared at him fiercely: "I'm afraid that others don't know that you are stingy."

Seeing that the situation was getting out of control, Wang Qi no longer accepted those sermons for low-level monks.

In order to avoid raising his positive reputation too high, causing all of Shenzhou to be his fans.

However, he did not prohibit other members of the foundation faction from doing so.