Geodesic
On reducibilities of numerations
Sbornik. Mathematics, Tome 40 (1981) no. 2, pp. 193-204

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If $\nu_0$ and $\nu_1$ are two numerations of the set $S$, then $\nu_0$ will be said to be $e$-reducible to $\nu_1$ provided there exists an enumeration operator $\Phi$ such that ($\forall s\in S$) $[\nu_0^{-1}(s)=\Phi(\nu_1^{-1}(s))]$. In this paper both $e$-reducibility and upper semilattices of $e$-equivalent computable families of recursively enumerable sets are studied. Some of these semilattices admit an elegant description; for others sufficient conditions are found in order that they have an $e$-principal numeration or be countable. Bibliography: 7 titles. 
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     author = {A. N. Degtev},
     title = {On reducibilities of numerations},
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A. N. Degtev. On reducibilities of numerations. Sbornik. Mathematics, Tome 40 (1981) no. 2, pp. 193-204. http://geodesic.mathdoc.fr/item/SM_1981_40_2_a4/