Numberings on Admissible Structures over Equivalence Relations
ISKANDER SH. KALIMULLIN, V. G. Puzarenko · Lobachevskii Journal of Mathematics · 2024
The paper gives a series of examples of admissible sets $$\mathbb{A}$$ in which the family of all $$\mathbb{A}$$ -c.e. sets has neither negative, nor positive computable $$\mathbb{A}$$ -numberings. In particular, it is proved that for hereditarily finite superstructures over negative partners of equivalence relations the family of all $$\Sigma$$ -subsets may have no negative computable numbering. An opposite result was established earlier for positive numberings and positive partners of equivalence relations [2, 4].