Arithmetical Reducibilities I
Arithmetical Reducibilities I
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算术约简 I
DOI：
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发表时间：
1971
期刊：
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通讯作者：
A. Selman
中科院分区：
文献类型：
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作者：
A. Selman
三维可约关系是自然数集合上的传递自反关系，使得对任意两个集合A和B，A&B蕴涵AeZ^.本文研究了两个层次的可约性，S，n < u）和S，n < a）.每个层次的可归约性具有其他层次所不具有的自然属性。每一个都是相对递归的推广，每一个S都具有ε集合类是S -度结构的性质，证明了关于这些可约性结构的各种定理。
A 3D - reductibility relation is defined to be a transitive and reflexive relation & on sets of natural numbers, so that for every two sets A and B, A&B implies AeZ^. Two hierarchies of such reducibilities are studied, & , n < u), and n S , n < a). The reducibilities of each hierarchy have natural properties not possessed by the other. Each generalizes relative recursion; each S has the property that the class of £ sets is the for the S -degree structure, Various theorems concerning the structure of these reducibilities are proved.