构造自然数算术系统的一种新方法

A New Method of Constructed Algorithm Systems on Natural Number

用公理化方法来定义非空集上的二元关系<,使得<与该集合构成全序集,在全序集中给出最小元素原理的定义,再构造一个含有最小元素原理的适当公理系统来重新给出自然数的公理化定义,然后从构造的自然数公理系统中严格推导出一些基本命题,最后根据这些基本命题来完成对自然数算术系统的精确刻画,从而得到一种具体构造自然算术系统的新方法。

In this paper, a definition of binary totally relation ＂〈＂ is given on set by using axiomatic methods, definition of principle of the least element is given on set. The author constructs an axiomatic system by using principle of the least dement as an axioms which gives a new definition of natural number. Then we deduce some elementary theorems titan axiomatic systems of natural number. Finally the author constructs algorithm systems of natural number by using these elementary theorems. So we find a new method of constructed algorithm systems on natural number.