Absolute and Relative Properties of Negatively Numbered Families
M. Kh. Faĭzrahmanov, V. G. Puzarenko · Lobachevskii Journal of Mathematics · 2021
We study in this paper negative $$\mathbb{A}$$ -numberings where $$\mathbb{A}$$ are admissible structures. We establish that a series of classical assumptions is remained to hold for negative $$\mathbb{A}$$ -numberings in the case of the application of certain limits as for numberings as for admissible structures. We find examples of admissible structures $$\mathbb{A}$$ whose families of all $$\Sigma$$ -subsets have negative non-decidable minimal computable $$\mathbb{A}$$ -numberings. The admissible structures from this series have negative computable $$\mathbb{A}$$ -numberings whose numbered equivalence differs from corresponding ones of any computable $$\mathbb{A}$$ -numbering of family of total functions.