Closed Sets and Enumerations
msra(2007)
摘要
An eectively closed set, or 0 1 class, may viewed as the set of infi- nite paths through a computable tree. A numbering, or enumeration, is a map from ! onto a countable collection of objects. One numbering is reducible to another if equality holds after the second is composed with a computable function. Many commonly used numberings of 0 1 classes are shown to be mutually reducible via a computable permutation. Com- putable injective numberings are given for the family of 0 1 classes and for the subclasses of decidable and of homogeneous 0 1 classes. However no computable numberings exist for small or thin classes. No computable numbering of trees exists that includes all computable trees without dead ends.
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关键词
numberings,computability,0 1 classes
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