直觉主义集合论的主要特征

发布时间：2018-03-21 03:18

本文选题：直觉主义集合论　切入点：策梅洛-弗兰克尔　出处：《学术交流》2017年08期 　论文类型：期刊论文

【摘要】：直觉主义集合论建立在直觉主义而不是经典逻辑之上,因此表现了一种基于直觉主义逻辑的、在其中编码和研究数学的自然环境。作为直觉主义集合论中的典型代表,直觉主义策梅洛-弗兰克尔集合论是建立在直觉主义逻辑上的策梅洛-弗兰克尔形式的公理化集合论,它基于仅以二元谓词符号"属于"作为其非逻辑符号的一阶语言,在带等词加上二元谓词符号"属于"的直觉主义一阶逻辑基础上公式化。因为对于直觉主义逻辑的承诺和对经典传统的背离,直觉主义集合论在集合论的性质、公理准则的选取和公理系统的建构上有其独特性。而为了更加深入精确地研究直觉主义集合论,需要用到大量的证明论和语义学技术。
[Abstract]:Intuitionistic collectivism is based on intuitionism rather than classical logic, so it represents a natural environment in which the code and study of mathematics is based on intuitionistic logic. The intuitionist Zimelo-Frankel set theory is an axiomatic set theory based on the intuitionistic logic. It is based on the first order language which only takes the binary predicate sign "belong" as its non-logical symbol. Formulations are formulated on the basis of the first-order logic of intuitionism, which includes words such as "belong", because of the nature of intuitionistic collectivism in its commitment to the logic of intuitionism and its deviation from classical tradition, The selection of axioms and the construction of axioms have their own uniqueness, but in order to study intuitionism collection theory more accurately, a large number of proofs and semantics techniques are needed.
【作者单位】：南开大学哲学院;
【分类号】：B815.9

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