Geodesic
Two theorems on minimal generally-computable numberings
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2023), pp. 28-35

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The paper proves that for any set $A$ that computes a non-computable computably enumerable set, any infinite $A$-computable family has an infinite number of pairwise nonequivalent minimal $A$-computable numberings. It is established that an arbitrary set $A\leqslant_T\emptyset '$ is low if and only if any infinite $A$-computable family with the greatest set under inclusion has an infinite number of pairwise nonequivalent positive $A$-computable numberings. 
@article{VMUMM_2023_3_a4,
     author = {M. Kh. Faizrahmanov},
     title = {Two theorems on minimal generally-computable numberings},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {28--35},
     publisher = {mathdoc},
     number = {3},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2023_3_a4/}
}
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M. Kh. Faizrahmanov. Two theorems on minimal generally-computable numberings. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 3 (2023), pp. 28-35. http://geodesic.mathdoc.fr/item/VMUMM_2023_3_a4/