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Erschienen in:
1987 | OriginalPaper | Buchkapitel
Creative, Productive, Complete Sets
verfasst von : Prof. Dr. Klaus Weihrauch
Erschienen in: Computability
Verlag: Springer Berlin Heidelberg
Enthalten in: Professional Book Archive
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As we already know the set K= {i | i ∈ dom(φi)} is recursively enumerable and not recursive. In the set RE of recursively enumerable subsets of N the set K has several characteristic remarkable properties: it is creative, it is m-complete, it is 1-complete, and its complement is the smallest productive set. As we shall see, creativity and productivity have interesting applications in logic. As a kind of generalization of creativity we finally introduce effective inseparability and prove a further generalization of Rice’s theorem for precomplete numberings.