What Wang Qi wanted to tell Feng Luoyi was, naturally, the Inner Model Plan.
Inner models and constructible classes were more or less like flowers and fruit. Constructible classes were the flowers; inner models were the fruit.
But inner models, after all, possessed fatal flaws.
First of all, they were built entirely upon well-founded sets. And there truly were parts of mathematics that could only be mastered with non-well-founded sets.
Moreover, they excluded cycles and contained no infinitely descending chains.
Additionally, they could not accommodate large cardinals, including the first and second inaccessible cardinals.
Large cardinals had many benefits. As mentioned before, introducing large cardinals could directly prove that any constructible set of real numbers would not trigger the sphere-division paradox, without needing to discard the axiom of choice; introducing large cardinals could prove the completeness of second-order arithmetic, and so on.
And if the theoretical system of the Foundation Establishment School wanted to develop, it too had to have large cardinals.
But inner models were not without merit.
The continuum problem could actually be considered a third-order problem. And large cardinals happened to be incapable of resolving third-order problems.
The Inner Model Method could resolve it perfectly.
Therefore, abandoning inner models for the sake of large cardinals would be the foolish act of picking up sesame seeds while losing a watermelon.
Thus, Wang Qi proposed an idea.
A very natural idea of "combining them and making piss balls."
Starting from an inner model, one would use the Forceful Method to continually add elements, expanding the mathematical model itself step by step until it could accommodate large cardinals.
The Forceful Method itself worked by continually adding elements, exposing the connections between two different sets, ultimately achieving the effect of "letting the theory prove itself."
The Inner Model Plan could be