In this paper, the notions of recursive functions and recursive formulas on sets are introduced; some properties of such functions and formulas are studied; and the relations between recursive set functions and primitively recursive set functions are defined by Jenson and Karp and between recursive set functions and recursive number theoretic functions are also discussed.
研究了递归集函数的初步性质，讨论了递归集函数与Ｊｅｎｓｅｎ和Ｋａｒｐ定义的原始递归集函数及递归数论函数之间的关系，并给出了ＺＦＣ的可定义集模型上递归集函数的范式定理。
The theorem that the language set distinguished deterministic finite automaton is a recursively enumerable set was proved,and then,the recursiveness of regular language was analyzed.
从正则语言识别的角度证明了正则语言的识别系统确定有限自动机所识别的语言集是一个递归可枚举集,同时讨论了正则语言的可递归性。