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On the autological character of diagonalizable algebras. (English) Zbl 0359.02027
Let \(J\) be the first order theory of diagonalizable algebras (for first concepts on d. a. see R. Magari [Boll. Un. mat. Ital., IV. Ser. 12, Suppl. Fasc. 3, 117-125 (1975; Zbl 0352.08009)]). The author defines a bijection \(\varphi\) from the identities of \(J\) to the open formulas of \(J\) and he proves that \(t_1=t_2\) is an identity of the diagonalizable algebras iff \(\varphi(t_1=t_2)\) is valid.

MSC:
03F99 Proof theory and constructive mathematics
08B99 Varieties
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