Abstract
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].
