Two Theorems on Minimal Generalized Computable Numberings
M. Kh. Faĭzrahmanov · Moscow University Mathematics Bulletin · 2023
The paper proves that for any set $$A$$ that computes a noncomputable 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 $$A\leqslant_{T}\emptyset^{\prime}$$ 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.