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

The algebraization of theories which express Theor; V

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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 numbern, then-freely generated algebraF 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 byF n .

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  1. Siena University, Siena, Italy

    Franco Montagna

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  1. Franco Montagna
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Allatum est die 21 Aprilis 1975

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Montagna, F. For everyn, then-freely generated algebra is not functionally free in the equational class of diagonalizable algebras. Stud Logica 34, 315–319 (1975). https://doi.org/10.1007/BF02121662

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