Nonstandard Arithmetic and Reverse Mathematics
Nonstandard Arithmetic and Reverse Mathematics
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非标准算术和逆向数学
DOI：
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发表时间：
2006
影响因子：
0.6
通讯作者：
H. Keisler
中科院分区：
文献类型：
--
作者：
H. Keisler
摘要我们证明了在逆向数学中起核心作用的五个二阶算术基本理论中的每一个在非标准算术语言中都有一个自然的对应物。在前面的文献[3]中，我们引入了非标准算术中的饱和原理，它与二阶算术中的强选择公理在强度上等价。本文研究了二阶算术中与较弱理论强度等价的原理。
Abstract We show that each of the five basic theories of second order arithmetic that play a central role in reverse mathematics has a natural counterpart in the language of nonstandard arithmetic. In the earlier paper [3] we introduced saturation principles in nonstandard arithmetic which are equivalent in strength to strong choice axioms in second order arithmetic. This paper studies principles which are equivalent in strength to weaker theories in second order arithmetic.