Numerazioni positive, r.e. classi e formule

In this paper we investigate some recursion-theoretic properties of the positive numerations induced by certain remarkable formulas of any theory T as strong as Peano Arithmetic: in particular we prove that any Sigma_n-truth predicate (in an appropriate sense) induces a precomplete positive numeration and that the formulas which preserve the provable equivalence induce u-m-v equivalence relations (and there exist formulas which induce u-m-c but not precomplete numerations). By means of theory of numerations, a classical result due to Putnam and Smullyan (1960) and redemonstrated by Smorynski (1978) is generalized.