Functional representation of finitely generated free algebras in subvarieties of BL-algebras

Annals of Pure and Applied Logic 171 (2):102757 (2020)
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Abstract

Consider any subvariety of BL-algebras generated by a single BL-chain which is the ordinal sum of the standard MV-algebra on [0, 1] and a basic hoop H. We present a geometrical characterization of elements in the finitely generated free algebra of each of these subvarieties. In this characterization there is a clear insight of the role of the regular and dense elements of the generating chain. As an application, we analyze maximal and prime filters in the free algebra.

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A theorem about infinite-valued sentential logic.Robert McNaughton - 1951 - Journal of Symbolic Logic 16 (1):1-13.
The free n -generated BL-algebra.Stefano Aguzzoli & Simone Bova - 2010 - Annals of Pure and Applied Logic 161 (9):1144-1170.
Geometry of Robinson consistency in Łukasiewicz logic.Manuela Busaniche & Daniele Mundici - 2007 - Annals of Pure and Applied Logic 147 (1):1-22.

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