浅议一阶逻辑的发展与集合论公理化的关系

On the Relationship between the Development of First-order Logic and the Axiomatization of Set Theory

众所周知,一阶逻辑与公理集合论是数理逻辑的两个组成部分,其中,一阶逻辑是数理逻辑的基础部分。但在数理逻辑刚刚出现的时候,逻辑不是一阶的,集合论也经历了由康托尔素朴集合论到公理集合论的发展。在数理逻辑发展的历史中,一阶逻辑的出现及其主导地位的确立与集合论的公理化,二者之间存在着密切的联系。

It is well known that first-order logic and axiom set theory are two part of the whole mathematical logic. However at the beginning of mathematical logic, logics were not first-order, and set theory has gone through from Kantor＇s naive set theory to axiom set theory. In the history of the development of mathematical logic, there has been close relationship between the emergence and dominance of first-order logic and the axiomatization of set theory.