It is well-known that, in Peano arithmetic, there exists a formulaTheor(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 ofTheor, 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 byTheor which are consequences of the known ones is decidable.
On the equational class of diagonalizable algebras. The algebraization of the theories which express Theor, VI / Bernardi, Claudio. - In: STUDIA LOGICA. - ISSN 0039-3215. - STAMPA. - 34:4(1975), pp. 321-331. [10.1007/bf02121663]
On the equational class of diagonalizable algebras. The algebraization of the theories which express Theor, VI.
BERNARDI, Claudio
1975
Abstract
It is well-known that, in Peano arithmetic, there exists a formulaTheor(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 ofTheor, 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 byTheor which are consequences of the known ones is decidable.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
