The compact theorem is proved, which states that theory T has model if and only if any finite subset of T has model.

利用中介逻辑的完备性，本文证明了紧致性定理，即一理论有模型当且仅当其任一有穷子集有模型。

youdao

And finally we prove that let a be a subset of real Numbers, if every continuous function which is defined on a and taken value in a has fixed point, then a is a finite closed interval.

最后还证明了对于实数的子集a，如果定义在A上取值于A内的任一连续函数都有不动点，则A为实数的有限闭区间。

youdao

Absrtact: the problem of repetitive computing exits in the process of transition from non-deterministic finite automata to deterministic finite automata using the subset construction method.

摘要：使用子集构造法对非确定有限自动机进行确定化的过程中存在大量重复计算的问题。

youdao