  We consider the problem of finding pre-fixed points of interactive realizers
over arbitrary knowledge spaces, obtaining a relative recursive procedure.
Knowledge spaces and interactive realizers are an abstract setting to represent
learning processes, that can interpret non-constructive proofs. Atomic pieces
of information of a knowledge space are stratified into levels, and evaluated
into truth values depending on knowledge states. Realizers are then used to
define operators that extend a given state by adding and possibly removing
atoms: in a learning process states of knowledge change nonmonotonically.
Existence of a pre-fixed point of a realizer is equivalent to the termination
of the learning process with some state of knowledge which is free of patent
contradictions and such that there is nothing to add. In this paper we
generalize our previous results in the case of level 2 knowledge spaces and
deterministic operators to the case of omega-level knowledge spaces and of
non-deterministic operators.
