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Decision Problems for Classes of Diagonalizable Algebras

Aldo Ursini
Studia Logica: An International Journal for Symbolic Logic
Vol. 44, No. 1 (1985), pp. 87-89
Published by: Springer
Stable URL: http://www.jstor.org/stable/20015200
Page Count: 3
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Decision Problems for Classes of Diagonalizable Algebras
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Abstract

We make use of a Theorem of Burris-McKenzie to prove that the only decidable variety of diagonalizable algebras is that defined by '$\tau 0=1$'. Any variety containing an algebra in which $\tau 0\supsetneqq 1$ is hereditarily undecidable. Moreover, any variety of intuitionistic diagonalizable algebras is undecidable.

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