对角线元素与不同复杂度的系统的关系  

On the Relations between Diagonal Elements and Systems of Different Complexities

作　　者：贾国恒[1] 

机构地区：[1]华东师范大学哲学系

出　　处：《哲学研究》2012年第6期112-115,128,共4页Philosophical Research

基　　金：教育部人文社会科学研究项目"面向信息处理的情境语义学研究"(编号08JC720016)和教育部人文社会科学重点研究基地重大项目"结构推理及其应用研究"(编号10JJD720010)资助

摘　　要：对角线方法是指德国学者康托尔（G．Cantor）在证明实数集不可数时所运用的一种技术方法。在这种意义上，康托尔的实数集不可数论本身便是对角线方法的一种重要运用。此外，对角线方法还有两种重要运用，即哥德尔对角线定理和汤姆逊引理的证明。There are four kinds of relations between diagonal elements and its system.Either no diagonal element can be constructed in a system,or though diagonal elements can be constructed and can be proved to be true in a system but they are not within the system,or they can be constructed and can be proved to be true within a system,or they can be constructed within a system but cannot be proved to be true or false within the system,and there must be one of the four cases.According to the constructions of diagonal elements,real number matrixes are more complex than that of first-order logic systems,but less complex than that of real number intervals or real number,and the latters are less complex than arithmetic systems.

关 键 词：对角线 复杂度 系统 元素 实数集 不可数 汤姆逊 哥德尔 

分 类 号：O157.2[理学—数学]