Reduction of computable and potentially computable numerations
Matematičeskie zametki, Tome 6 (1969) no. 1, pp. 3-9
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Among the numerations of classes of countable sets there can be distinguished those in which the number contains information about the set having the number — these are computable and potentially computable numerations — and those in which the set contains information about its number — these are covering and fully covering numerations. The conditions are established which are necessary and sufficient in order that all numerations of the given class should be covering. As a corollary it is established that there exist covering numerations which are not fully covering.