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 10.1007/BF02121663
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Solution of a Problem of Leon Henkin.M. H. Lob - 1955 - Journal of Symbolic Logic 20 (2):115-118.
Universal Algebra.George Grätzer - 1982 - Studia Logica 41 (4):430-431.

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Varieties of Complex Algebras.Robert Goldblatt - 1989 - Annals of Pure and Applied Logic 44 (3):173-242.
An Algebraic Study of Well-Foundedness.Robert Goldblatt - 1985 - Studia Logica 44 (4):423 - 437.

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