an:01775504
Zbl 1014.06008
Georgescu, George; Iorgulescu, Afrodita
Pseudo-MV algebras
EN
Mult.-Valued Log. 6, No. 1-2, 95-135 (2001).
00087453
2001
j
06D35 03B50 03G25 06F15
categorical equivalence; pseudo-MV algebra; l-group; normal ideal; Boolean center; Boolean sheaf; Pierce sheaves; Pierce representations
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 \textit{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 \textit{R. L. O. Cignoli, I. M. L. D'Ottaviano} and \textit{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.
Vladimir Komendantsky (Dolgoprudny)
Zbl 0084.00704; Zbl 0937.06009