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The uniqueness of the fixed-point in every diagonalizable algebra (1976)

Bernardi, Claudio

Springer

Studia logica 35 (1976), S. 335-343

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ISSN: 1572-8730

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics , Philosophy

Notes: Summary It is well known that, in Peano arithmetic, there exists a formulaTheor (x) which numerates the set of theorems. By Gödel's and Löb's results, we have that Therefore, the considered «equations» admit, up to provable equivalence, only one solution. In this paper we prove (Corollary 1), that, in general, ifP (x) is an arbitrary formula built fromTheor (x), then the fixed-point ofP (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).

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF02123401

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