For everyn, then-freely generated algebra is not functionally free in the equational class of diagonalizable algebras

Studia Logica 34 (4):315 - 319 (1975)
This paper is devoted to the algebraization of theories in which, as in Peano arithmetic, there is a formula, Theor(x), numerating the set of theorems, and satisfying Hilbert-Bernays derivability conditions. In particular, we study the diagonalizable algebras, which are been introduced by R. Magari in [6], [7]. We prove that for every natural number n, the n-freely generated algebra $\germ{J}_{n}$ is not functionally free in the equational class of diagonalizable algebras; we also prove that the diagonalizable algebra of Peano arithmetic is not an element of the equational class generated by $\{\germ{J}_{n}\}$
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DOI 10.2307/20014776
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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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