Reduction of computable and potentially computable numerations

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.