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Some effectively infinite classes of enumerations. (English) Zbl 0783.03022
Summary: This research partially answers the question raised by Goncharov about the size of the class of positive elements of a Rogers semilattice. We introduce a notion of effective infinity of classes of computable enumerations. Then, using finite injury priority method, we prove five theorems which give sufficient conditions to be effectively infinite for classes of all enumerations without repetitions, positive undecidable enumerations, negative undecidable enumerations and all computable enumerations of a family of r.e. sets. These theorems permit to strengthen the results of Pour-El, Howard, Ershov and Khutoretskij about existence of enumerations without repetitions and positive undecidable enumerations.
MSC:
03D45 Theory of numerations, effectively presented structures
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References:
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