Comparing Pi^0_2 of the Baire space by means of general recursive operators

By applying a notion of reducibility suggested by DiPaola and Heller to the domains of a recursion category previously introduced by ourselves, we get many-one reducibility between PI-2(0) sets of the arithmetical hierarchy of sets of functions by means of general recursive operators. We give a characterization of the complete domains in this reducibility. We also introduce an upper semilattice B to which this reducibility gives rise in a standard way. Several facts about B are proved: we characterize the finite ideals of B; the first order theory of B is shown to be undecidable.