Computably separable numbering of locally finitely separable algebras

It has been establish that the locally finitely separability of any universal algebra represented over a given uniformly computably separable equivalence is equivalent to the immune of the characteristic transversal of this equivalence. Examples are presented that demonstrate the infidelity of this criterion for finitely separable algebras, as well as for computably separable equivalences that are not uniform. It is shown that every infinite and co-infinite set is a characteristic transversal of a computably separable equivalence, over which only finitely approximable algebras are represented.