RELATIVE PREDICATIVITY AND DEPENDENT RECURSION IN SECOND-ORDER SET THEORY AND HIGHER-ORDER THEORIES
RELATIVE PREDICATIVITY AND DEPENDENT RECURSION IN SECOND-ORDER SET THEORY AND HIGHER-ORDER THEORIES
复制标题
二阶集合论和高阶理论中的相对预测性和相关递归
DOI：
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发表时间：
2014
期刊：
影响因子：
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通讯作者：
Sato Kentaro
中科院分区：
文献类型：
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作者：
Sato Kentaro
摘要本文报道，如果我们选择一些不同于传统ω的数学实体作为给定的无限总实体，则预测性概念和自主级数概念的一些稳健性被打破。也就是说，正规超限递归格式和新的相依超限递归格式之间的等价性在二阶集合论的子系统的上下文中不成立，其中集合的宇宙V被视为给定的总体(或者在n+3阶数或集合论的上下文中，其中所有n+2阶对象的类被视为给定的总体)。
Abstract This article reports that some robustness of the notions of predicativity and of autonomous progression is broken down if as the given infinite total entity we choose some mathematical entities other than the traditional ω. Namely, the equivalence between normal transfinite recursion scheme and new dependent transfinite recursion scheme, which does hold in the context of subsystems of second order number theory, does not hold in the context of subsystems of second order set theory where the universe V of sets is treated as the given totality (nor in the contexts of those of n+3-th order number or set theories, where the class of all n+2-th order objects is treated as the given totality).
集合论中的类和真理
影响因子：
0.8
作者：
Fujimoto K
通讯作者：
Fujimoto K