A comparison of concepts from computable analysis and effective descriptive set theory
A comparison of concepts from computable analysis and effective descriptive set theory
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可计算分析和有效描述集合论概念的比较
DOI：
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发表时间：
2014
影响因子：
0.5
通讯作者：
A. Pauly
中科院分区：
文献类型：
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作者：
Vassilios Gregoriades;Tamás Kispéter;A. Pauly
可计算分析和有效描述集合论都是研究完备度量空间、完备度量空间之间的函数以及完备度量空间在有效集合中的子集。迄今为止，这两个学科中使用的各种定义的确切关系一直被忽视，本文旨在纠正这种情况。由于柯西完备性的作用与波兰空间的两种有效方法相关，我们将更详细地考虑有效性和完备性的相互作用。
Computable analysis and effective descriptive set theory are both concerned with complete metric spaces, functions between them and subsets thereof in an effective setting. The precise relationship of the various definitions used in the two disciplines has so far been neglected, a situation this paper is meant to remedy. As the role of the Cauchy completion is relevant for both effective approaches to Polish spaces, we consider the interplay of effectivity and completion in some more detail.