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A Generalization of the Łukasiewicz Algebras

Teresa Almada and Júlia Vaz de Carvalho
Studia Logica: An International Journal for Symbolic Logic
Vol. 69, No. 3 (Dec., 2001), pp. 329-338
Published by: Springer
Stable URL: http://www.jstor.org/stable/20016355
Page Count: 10
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A Generalization of the Łukasiewicz Algebras
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Abstract

We introduce the variety $\scr{L}_{n}^{m}$, m ≥ 1 and n ≥ 2, of m-generalized Łukasiewicz algebras of order n and characterize its subdirectly irreducible algebras. The variety $\scr{L}_{n}^{m}$ is semisimple, locally finite and has equationally definable principal congruences. Furthermore, the variety $\scr{L}_{n}^{m}$ contains the variety of Łukasiewicz algebras of order n.

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