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Free algebras in varieties of Stonean residuated lattices

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Abstract

Given a variety \(\mathbb{V}\) of bounded residuated lattices satisfying the Stone identity \(\neg x \lor \neg\neg x = \top\), the free algebras in \(\mathbb{V}\) over a set X of cardinality |X| are represented as weak Boolean products over the Cantor space 2|X| of a family of free algebras in an associated variety of (not necessarily bounded) residuated lattices with a bottom added.

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  1. Instituto Argentino de Matemática—CONICET, Saavedra 15, Piso 3, 1083, Buenos Aires, Argentina

    Roberto Cignoli

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  1. Roberto Cignoli
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Correspondence to Roberto Cignoli.

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Cignoli, R. Free algebras in varieties of Stonean residuated lattices. Soft Comput 12, 315–320 (2008). https://doi.org/10.1007/s00500-007-0183-x

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