| 完美数与亲和数问题对PA的条件独立性——对一些数论问题的逻辑讨论(Ⅲ) |
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| 引用本文： | 王世强.完美数与亲和数问题对PA的条件独立性——对一些数论问题的逻辑讨论(Ⅲ)[J].北京师范大学学报(自然科学版),2002,38(3):310-312. |
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| 作者姓名： | 王世强 |
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| 作者单位： | 北京师范大学数学系,北京,100875 |
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| 基金项目： | 国家自然科学基金;19931020; |
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| 摘 要： | 用模型论方法证明了,对于在自然数系N上与PA等价的一组公理P1而言,N中一类特殊完美数的无限性是独立于P1 的. 并且,N中一类特殊亲和数的无限性也是独立于P1的.
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| 关 键 词： | 完美数 亲和数 Peano公理组 模型论 |
| 修稿时间： | 2002年1月14日 |
CONDITIONAL INDEPENDENCE TO PA OF THE PROBLEMS ON PERFECT NUMBERS AND AMICABLE NUMBERS --LOGICAL DISCUSSIONS ABOUT SOME PROBLEMS IN NUMBER THEORY (Ⅲ) |
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| Wang Shiqiang.CONDITIONAL INDEPENDENCE TO PA OF THE PROBLEMS ON PERFECT NUMBERS AND AMICABLE NUMBERS --LOGICAL DISCUSSIONS ABOUT SOME PROBLEMS IN NUMBER THEORY (Ⅲ)[J].Journal of Beijing Normal University(Natural Science),2002,38(3):310-312. |
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| Authors: | Wang Shiqiang |
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| Abstract: | It is shown by model theoretic methods that, for a set of axioms P 1 which is equivalent to PA over the system N of natural numbers, the infinitude of a special kind of perfect numbers in N is independent to P 1. Also, the infinitude of a special kind of pairs of amicable numbers in N is independent of P 1. |
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| Keywords: | perfect number amicable numbers Peano axioms model theory |
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