| 论Ⅰ、Ⅱ型数学归纳原理及良序原理之间的逻辑关系 |
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| 引用本文： | 黄崇智. 论Ⅰ、Ⅱ型数学归纳原理及良序原理之间的逻辑关系[J]. 内江师范学院学报, 2003, 18(6): 59-64 |
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| 作者姓名： | 黄崇智 |
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| 作者单位： | 内江师范学院,数学系,四川,内江,641112 |
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| 摘 要： | 本包含两个部份。其一详论在一定条件下，I、Ⅱ型数学归纳原理及良序原理之间的逻辑关系：另一则提供一个关于自然数集N的公理并论证它与Peano公理系统的等价性。
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| 关 键 词： | 数学归纳原理 良序原理 全序整环 全序集 Peano公理 代数运算 |
| 文章编号： | 1671-1785(2003)06-0059-06 |
| 修稿时间： | 2003-09-01 |
On the Logical Relation between the First as well as the Second Principle of Mathematical Induction and the Well-Ordering Principle |
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| HUANG Chong-zhi. On the Logical Relation between the First as well as the Second Principle of Mathematical Induction and the Well-Ordering Principle[J]. Journal of Neijiang Teachers College, 2003, 18(6): 59-64 |
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| Authors: | HUANG Chong-zhi |
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| Abstract: | This paper consists of two parts. One of them deals detailedly with the logical relation between the principle of mathematical induction (type I sa well as type I )and the well-ordering principle under a certain condition and the other introduces an axiom concerning the natural numbers and demonstrates the equivalence between it and the system of Peano axioms. |
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| Keywords: | principle of mathematical induction well-ordering principle ordered integral domain ordered set Peano axioms algebraic operations |
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