It is well known that, in Peano arithmetic, there exists a formula Theor (x) which numerates the set of theorems. In this paper we prove (Corollary 1), that, in general, if P (x) is an arbitrary formula built fromTheor (x), then the fixed-point of P (x) (which exists by the diagonalization lemma) is unique up to provable equivalence. This result is settled referring to the concept of diagonalizable algebra (see Introduction).
The uniqueness of the fixed-point in every diagonalizable algebra. The algebraization of the theories which express Theor, VIII / Bernardi, Claudio. - In: STUDIA LOGICA. - ISSN 0039-3215. - STAMPA. - 35:(1976), pp. 335-343. [10.1007/BF02123401]
The uniqueness of the fixed-point in every diagonalizable algebra. The algebraization of the theories which express Theor, VIII
BERNARDI, Claudio
1976
Abstract
It is well known that, in Peano arithmetic, there exists a formula Theor (x) which numerates the set of theorems. In this paper we prove (Corollary 1), that, in general, if P (x) is an arbitrary formula built fromTheor (x), then the fixed-point of P (x) (which exists by the diagonalization lemma) is unique up to provable equivalence. This result is settled referring to the concept of diagonalizable algebra (see Introduction).I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
