Recursive labelling systems and stability of recursive structures in hyperarithmetical degrees

We show that, under certain assumptions of recursiveness in 2t, the recursive structure 2t is AO-stable for ca w, we need to deal with limit ordinals, and we frame an analogous result [Proposition 2] for (-yn)-systems where (-yn) is an increasing sequence of ordinals. Propositions 1 and 2 are then established by the