Set theoretic foundations for constructive analysis
Set theoretic foundations for constructive analysis
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为建设性分析奠定理论基础
DOI：
10.2307/1971023
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发表时间：
1977
影响因子：
4.9
通讯作者：
H. Friedman
中科院分区：
文献类型：
--
作者：
H. Friedman
我们介绍了一个扩展的集合论形式主义B，Zermelo集理论的一个子系统的直觉逻辑的基础上，它提供了一个集理论基础建设性的分析，这是惊人的类似于通常的集合论基础，普通的分析。我们证明了B具有相同的初等（LL？）结论作为一阶算术，并且B的每个算术结论都是Peano算术的结论。我们指出B的一个定义翻译为一个内涵理论的谓词，这反过来又有一个自然的解释，在非形式理论
We introduce an extensional set theoretic formalism B, a subsystem of Zermelo set theory based on intuitionistic logic, which provides a set theoretic foundation for constructive analysis which is strikingly analogous to the usual set theoretic foundations for ordinary analysis. We prove that B has the same elementary (LL?) consequences as first order arithmetic, and that every arithmetic consequence of B is a consequence of Peano arithmetic. We indicate a definitional translation of B into an intensional theory of predicates, which in turn has a natural interpretation in the informal theory