One chain generated varieties of MV-algebras
In his paper ``Free products in the category of abelian \(l\)-groups with strong unit'' [J. Algebra 113, No. 1, 89-109 (1988; Zbl 0658.06010)], the present reviewer established the amalgamation property for the variety of Chang's MV-algebras. The latter are the Lindenbaum algebras of the infinite-valued Łukasiewicz logic and are deeply related to abelian lattice-orderd groups and also to AF \(C^*\)-algebras. For a comprehensive account see the monograph of \textit{R. Cignoli, I. M. L. D'Ottaviano} and \textit{D. Mundici} [Algebraic foundations of many-valued reasoning (Trends in Logic -- Studia Logica Library 7, Kluwer, Dordrecht) (2000; Zbl 0937.06009)]. Komori gave a complete classification of the subvarieties of MV-algebras. In the present paper, the authors prove that a subvariety has the amalgamation property iff it is generated by precisely one MV-chain. They also introduce a notion of ``abstract conditional space'', proving its equivalence with the notion of Post algebra of order 2.
scientific article; zbMATH DE number 1429463