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The Barwise-Schlipf theorem
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2020-10-20 , DOI: 10.1090/proc/15216 Ali Enayat , James H. Schmerl
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2020-10-20 , DOI: 10.1090/proc/15216 Ali Enayat , James H. Schmerl
Abstract:In 1975 Barwise and Schlipf published a landmark paper whose main theorem asserts that a nonstandard model 
of 
(Peano arithmetic) is recursively saturated iff 
has an expansion that satisfies the subsystem 
- 
of second order arithmetic. In this paper we identify a crucial error in the Barwise-Schlipf proof of the right-to-left direction of the theorem, and we offer a correct proof of the problematic direction.
中文翻译：
Barwise-Schlipf定理
摘要：1975 Barwise和Schlipf发表了划时代的论文，其主要定理断言非标准模型的（皮亚诺算术）被递归饱和当且仅当有一个扩展，其满足子系统-二阶算术。在本文中，我们确定了定理从右到左方向的Barwise-Schlipf证明中的一个关键错误，并且为有问题的方向提供了正确的证明。
更新日期：2020-11-12
of (Peano arithmetic) is recursively saturated iff has an expansion that satisfies the subsystem - of second order arithmetic. In this paper we identify a crucial error in the Barwise-Schlipf proof of the right-to-left direction of the theorem, and we offer a correct proof of the problematic direction. 中文翻译：
Barwise-Schlipf定理
摘要：1975 Barwise和Schlipf发表了划时代的论文，其主要定理断言非标准模型的（皮亚诺算术）被递归饱和当且仅当有一个扩展，其满足子系统-二阶算术。在本文中，我们确定了定理从右到左方向的Barwise-Schlipf证明中的一个关键错误，并且为有问题的方向提供了正确的证明。
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