Abstract

It is well-known that, in Peano arithmetic, there exists a formula Theor (x) which numerates the set of theorems and that this formula satisfies Hilbert-Bernays derivability conditions. Recently R. Magari has suggested an algebraization of the properties of Theor, introducing the concept of diagonalizable algebra (see [7]): of course this algebraization can be applied to all these theories in which there exists a predicate with analogous properties. In this paper, by means of methods of universal algebra, we study the equational class of diagonalizable algebras, proving, among other things, that the set of identities satisfied by Theor which are consequences of the known ones is decidable