This paper is devoted to the algebraization of an arithmetical predicate introduced by S. Feferman. To this purpose we investigate the equational class of Boolean algebras enriched with an operation (g=rtail), which translates such predicate, and an operation τ, which translates the usual predicate Theor. We deduce from the identities of this equational class some properties of (g=rtail) and some ties between (g=rtail) and τ; among these properties, let us point out a fixed-point theorem for a sufficiently large class of (...) (g=rtail)-τ polynomials. The last part of this paper concerns the duality theory for (g=rtail)-τ algebras. (shrink)