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A note on interval MV-algebras. (English) Zbl 1164.06010
MV-algebras were introduced by C. C. Chang to give a proof of the completeness theorem for Łukasiewicz infinite-valued propositional logic. For background see the monograph [R. L. O. Cignoli, I. M. L. D’Ottaviano and D. Mundici, Algebraic foundations of many-valued reasoning. Dordrecht: Kluwer (2000; Zbl 0937.06009)]. In the paper under review the authors equip intervals \([x,y]\) in any MV-algebra with suitable operations, and show that the resulting structures are MV-algebra.

06D35 MV-algebras
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[1] CIGNOLI R. L. O.-D’OTTAVIANO I. M. L.-MUNDICI D.: Algebraic Foundations of Many-valued Reasoning. Kluwer Acad. Publ., Dordrecht-Boston-London, 2000. · Zbl 0937.06009
[2] CHANG C. C.: Algebraic analysis of many valued logics. Trans. Amer. Math. Soc. 88 (1958), 467-490. · Zbl 0084.00704
[3] CHAJDA I.-HALAŠ R.-KÜHR J.: Distributive lattices with sectionally antitone involutions. Acta Sci. Math. (Szeged) 71 (2005), 19-33. · Zbl 1099.06006
[4] CHAJDA I.-HALAŠ R.-KÜHR J.: Implication in MV-algebras. Algebra Universalis 52 (2004), 377-382. · Zbl 1097.06011
[5] MUNDICI D.: Interpretation of AF C* -algebras in Lukasiewicz sentential calculus. J. Funct. Anal. 65 (1986), 15-63. · Zbl 0597.46059
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