DECIDABILITY AND UNDECIDABILITY OF THEORIES WITH A PREDICATE FOR THE PRIMES

被引：15
|
作者：
BATEMAN, PT [1 ]
JOCKUSCH, CG [1 ]
WOODS, AR [1 ]
机构：
[1] UNIV WESTERN AUSTRALIA,DEPT MATH,NEDLANDS,WA 6009,AUSTRALIA
来源：
JOURNAL OF SYMBOLIC LOGIC | 1993年 / 58卷 / 02期
关键词：
D O I：
10.2307/2275227
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
It is shown, assuming the linear case of Schinzel's Hypothesis, that the first-order theory of the structure <omega; +, P>, where P is the set of primes, is undecidable and, in fact, that multiplication of natural numbers is first-order definable in this structure. In the other direction, it is shown, from the same hypothesis, that the monadic second-order theory of <omega; S, P> is decidable, where S is the successor function. The latter result is proved using a general result of A. L. Semenov on decidability of monadic theories, and a proof of Semenov's result is presented.
引用
收藏
页码：672 / 687
页数：16
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