On the equational class of diagonalizable algebras

Studia Logica 34 (4):321 - 331 (1975)
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
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DOI 10.2307/20014777
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References found in this work BETA
M. H. Lob (1955). Solution of a Problem of Leon Henkin. Journal of Symbolic Logic 20 (2):115-118.
George Grätzer (1982). Universal Algebra. Studia Logica 41 (4):430-431.

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Robert Goldblatt (1989). Varieties of Complex Algebras. Annals of Pure and Applied Logic 44 (3):173-242.

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