集合上的递归函数

Recursive Set Functions

中文关键词:  递归集函数  递归集论公式  原始递归集函数

英文关键词:recursive set functions  recursive formulas on sets  primitively recursive set functions.

中文摘要:

      本文在Ｊｅｎｓｅｎ和Ｋａｒｐ工作的基础上引进了集合上的递归函数的概念．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．

英文摘要:

      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. The paper concludes with the Normal Form Theorem for recursive set functions.