一类素数问题等对PA的条件独立性——对一些数论问题的逻辑讨论(Ⅳ)  

CONDITIONAL INDEPENDENCE TO PA OF A CLASS OF PROBLEMS ABOUT PRIME NUMBERS AND OTHERS: LOGICAL DISCUSSIONS ABOUT SOME PROBLEMS IN NUMBER THEORY (Ⅳ)

作　　者：王世强[1] 别荣芳[2] 

机构地区：[1]北京师范大学数学系,北京100875 [2]北京师范大学信息学院,北京100875

出　　处：《北京师范大学学报（自然科学版）》2004年第5期579-581,共3页Journal of Beijing Normal University(Natural Science)

基　　金：国家自然科学基金重点资助项目 (199310 2 0 );国家自然科学 (青年 )基金资助项目 (10 0 0 10 0 6)

摘　　要：用模型论方法证明了 2次函数素数值问题及一种 3重完美数问题对于PA的条件独立性 ,以及一些更一般的结论 .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 and for certain first-order formula-tions of the following problems, the infinitude of prime values of certain quadratic functions on N is independent to P 1. Also, the infinitude of a special kind of 3-fold perfect numbers in N is independent to P 1. Much wider conclusions can also be drawn from the proofs.

关 键 词：2次函数素数值 多重完美数 Peano公理组 模型论 

分 类 号：O141.4[理学—数学]