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)

CONDITIONAL INDEPENDENCE TO PA OF THE PROBLEMS ON PERFECT NUMBERS AND AMICABLE NUMBERS --LOGICAL DISCUSSIONS ABOUT SOME PROBLEMS IN NUMBER THEORY (Ⅲ)

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 .

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.