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Pseudo-MV algebras. (English) Zbl 1014.06008
The authors present a precise analysis of pseudo-MV algebras which are categorically equivalent to arbitrary lattice-ordered groups. The notion of pseudo-MV algebra is a generalization of the notion of MV-algebra. Like the classical article of C. C. Chang [Trans. Am. Math. Soc. 88, 467-490 (1958; Zbl 0084.00704)], this paper is foundational as much as possible. The terminology and the problem set is close to the monograph of R. L. O. Cignoli, I. M. L. D’Ottaviano and D. Mundici [Algebraic foundations of many-valued reasoning. Trends in Logic – Studia Logica Library. 7. Dordrecht: Kluwer Academic Publishers (2000; Zbl 0937.06009)]. Moreover, in addition to those problems, a very influential section of this paper is contributed to the study of Pierce sheaves associated with pseudo-MV algebras, and Pierce representations of pseudo-MV algebras. The paper contains a number of open problems.

06D35 MV-algebras
03B50 Many-valued logic
03G25 Other algebras related to logic
06F15 Ordered groups