| Goldbach猜想等与PA的一些联系——对一些数论问题的逻辑讨论(Ⅱ) |
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| 引用本文： | 王世强.Goldbach猜想等与PA的一些联系——对一些数论问题的逻辑讨论(Ⅱ)[J].北京师范大学学报(自然科学版),2002,38(2):183-186. |
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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,100875,北京 |
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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Goldbach猜想和孪生素数猜想等的一些形式都独立于一组公理P1(而P1在自然数系N上与Peano公理组PA等价). 又证明了它们与一组较强的公理P2相和谐(P2也在N上与PA等价).
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| 关 键 词： | Goldbach猜想 孪生素数猜想 Peano公理组 模型论 |
| 修稿时间： | 2001年11月20日 |
SOME CONNECTIONS OF GOLDBACH CONJECTURE AND OTHERS WITH PA--LOGICAL DISCUSSIONS ABOUT SOME PROBLEMS IN NUMBER THEORY (Ⅱ) |
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| Wang Shiqiang.SOME CONNECTIONS OF GOLDBACH CONJECTURE AND OTHERS WITH PA--LOGICAL DISCUSSIONS ABOUT SOME PROBLEMS IN NUMBER THEORY (Ⅱ)[J].Journal of Beijing Normal University(Natural Science),2002,38(2):183-186. |
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| Authors: | Wang Shiqiang |
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| Abstract: | It is proved by model theoretic methods that some forms of Goldbach conjecture, the twin primes conjecture and others are independent to a set P 1 of axioms (while P 1 is equivalent to PA over the system N of natural numbers). Also, their consistency with a stronger set P 2 of axioms (which is also equivalent to PA over N) is proved. |
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| Keywords: | Goldbach conjecture twin primes conjecture Peano axioms model theory |
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