Categories and varieties of MV-algebras (Q2737554)

The author surveys a number of results on MV-algebras -- the algebras of the Łukasiewicz infinite-valued calculus. For instance, every MV-algebra is an algebra of \([0,1]^*\)-valued functions over some set, where \([0, 1]^*\) is an ultrapower of the unit real interval [see the author's paper in Ric. Mat. 40, 291-297 (1991; Zbl 0767.06013)]. Further, he discusses his own characterization of MV-algebraic equivalents of lattice-ordered groups, as well as axiomatizations of subvarieties of MV-algebras. The starting points of this paper are \textit{Y. Komori}'s classification of MV-algebraic varieties [Nagoya Math. J. 84, 119-133 (1981; Zbl 0482.03007)] and the present reviewer's categorical equivalence between MV-algebras and lattice-ordered abelian groups with strong unit [J. Funct. Anal. 65, 15-63 (1986; Zbl 0597.46059)],NEWLINENEWLINEFor the entire collection see [Zbl 0938.00016].