One note on positive A-computable numberings

Abstract

A family of finite sets is said to be strongly coverable if it has a subfamily with the computable set of canonical indices, such that every set of the coverable family is a subset of some set of the covering subfamily. We prove that a set [Formula: see text] is low if and only if every finite strongly coverable [Formula: see text]-computable family has a positive [Formula: see text]-computable numbering. We also show that in the previous criterion the strong coverability of a finite family cannot be skipped.