What is the Set
What is the Set
复制标题
什么是套装
DOI：
10.1111/1541-4329.12075
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发表时间：
2010
期刊：
影响因子：
--
通讯作者：
Yao Cong
中科院分区：
文献类型：
--
作者：
Yao Cong
坎太尔关于集合的定义通常被用来证明ZFC，它对集合有两种主要的解读：大小限制概念和迭代概念。大小限制概念理解集合与其大小相关的统一性或事物，但它既不为基础公理也不为幂集合公理辩护。迭代集合公理对集合的形成施加了时间限制，它证明了分离公理和幂集合公理，但它没有对替换公理提供解释。最自然的方法是对迭代公理施加大小限制，结构概念认为集合是一种展开可能结构的模式，因此集合的同一性应该由它们的分析模式的同一性来给出。在这个概念下，没有理由将可能的结构限制在有理有据的结构上。
The Cantorian definition of sets,which are commonly used to justify ZFC,has two main readings for sets: the limitation-of-size conception and iterative conception.The limitation-of-size conception understands the unity or the thingness of a collection as related to its size,but it offers no justification for either the foundation axiom or the power-set axiom.The iterative idea of set imposes a temporal restriction on the set-formation,and it justifies separation axiom and power set axiom,but it fails to offer an explanation for replacement axiom.The most natural way to do it would be to impose a limitation-of-size on the iterative,which can explain replacement,axiom but fails to justify power set axiom.Structural conception considers set as a pattern of unfolding a possible structure,so the identity of sets should be given by the identity of their analytical patterns.Under this conception there is no reason to limit the possible structure to the well-founded one.