  Different constructions in the recursion theory use the so-called priority
arguments. A general scheme was suggested by A.~Lachlan. Based on his work, we
define the notion of a priority-closed class of requirements. Then, for a
specific priority construction, we need to check only that all requirements we
want to satisfy belong to some priority-closed class (defined in game terms).
This game version of Lachlan's approach is used to present some results about
recursively inseparable sets obtained by the author.
