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《Journal of Beijing Normal University(Natural Science)》 2005-04
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ON THE ABUNDANCE OF THE INDUCTIVE EXTENSIONS OF THE RING OF INTEGERS WITH INFINITELY MANY n-PRIME TUPLES

Bie Rongfang(College of Information Science, Beijing Normal University, 100875, Beijing, China)  
It is shown by model-theoretic methods that the following results are valid for any positive integer n and any possible type of n-prime tuples: 1 There exist uncountably infinitely many inductive extensions of the ring I of integers with infinitely many such n-prime tuples(called nT-rings in the following)and these rings are not equivalent to each other in first order logic. 2 There exist infinitely many couples of positive integers such that for each couple(a, b), there exists an nT-ring R which satisfies the inductive principle with step a and does not satisfy the inductive principle with step b. 3 There exist nT-rings R such that every element of R is a sum of 3 squares and a sum of 4 cubes.
【Fund】: 国家自然科学基金重点资助项目(19931020);; 国家自然科学(青年)基金资助项目(60273015 10001006)
【CateGory Index】: O153.3
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【References】
Chinese Journal Full-text Database 1 Hits
1 MA Xin1,2) SHEN Fuxing1)(1)College of Mathematical Sciences,Beijing Normal University,100875,Beijing,China;2)College for Sciences,Gansu Agricultural University,730070,Lanzhou,China);THE CONDITIONAL INDEPENDENCE OF THREE PRIME TUPLES CONJECTURE WITH RESPECT TO PEANO AXIOMS[J];Journal of Beijing Normal University(Natural Science);2008-04
【Citations】
Chinese Journal Full-text Database 1 Hits
1 Wang Shiqiang 1) Bie Rongfang 2) ( 1)Department of Mathematics, Beijing Normal University , 100875, Beijing, China; 2) College of Information Science,Beijing Normal University, 100875, Beijing, China)$$$$;CONDITIONAL INDEPENDENCE TO PA OF A CLASS OF PROBLEMS ABOUT PRIME NUMBERS AND OTHERS: LOGICAL DISCUSSIONS ABOUT SOME PROBLEMS IN NUMBER THEORY (Ⅳ)[J];Journal of Beijing Normal University(Natural Science);2004-05
【Co-references】
Chinese Journal Full-text Database 1 Hits
1 Wang Shiqiang (Department of Mathematics, Beijing Normal University, 100875, Beijing, China);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);2002-02
【Secondary Citations】
Chinese Journal Full-text Database 2 Hits
1 Wang Shiqiang (Department of Mathematics, Beijing Normal University, 100875, Beijing, China);THE CONDITIONAL INDEPENDENCE OF GOLDBACH CONJECTURE WITH RESPECT TO PEANO AXIOMS ──LOGICAL DISCUSSIONS ABOUT SOME PROBLEMS IN NUMBER THEORY (Ⅰ)[J];Journal of Beijing Normal University(Natural Science);2001-04
2 Wang Shiqiang (Department of Mathematics, Beijing Normal University, 100875, Beijing, China);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);2002-03
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