Abstract
Under study is the problem of existence of minimal and strong minimal coverings in Rogers semilattices of \(\Sigma _n^0 \)-computable numberings for n≥2. Two sufficient conditions for existence of minimal coverings and one sufficient condition for existence of strong minimal coverings are found. The problem is completely solved of existence of minimal coverings in Rogers semilattices of \(\Sigma _n^0 \)-computable numberings of a finite family.
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Badaev, S.A., Podzorov, S.Y. Minimal Coverings in the Rogers Semilattices of∑-Computable Numberings. Siberian Mathematical Journal 43, 616–622 (2002). https://doi.org/10.1023/A:1016364016981
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DOI: https://doi.org/10.1023/A:1016364016981