Completeness and minimal covers of arithmetical numberings
M. Kh. Faĭzrahmanov · 2023
The paper studies Σ-0-n-computable families (n ⩾ 2) and their numberings. It is proved that any non-trivial Σ-0-n-computable family has a complete with respect to any of its elements Σ-0-n-computable non-principal numbering. It is established that if a Σ-0-n-computable family is not principal, then any of its Σ-0-n-computable numberings has a minimal cover.