Duality theory and skeleta for semisimple MV-algebras
This is a continuation of the paper by the same authors [``The skeletons of \(l\)-\(u\) groups and of MV-algebras'' (submitted)]. In their paper [Stud. Log. 100, No. 1--2, 253--278 (2012; Zbl 1252.06006)],\textit{V. Marra} and \textit{L. Spada} constructed a duality between semisimple MV-algebras and closed subsets of the Tychonov cube \([0,1]^\mu\) with \(\mu\) ranging over all cardinals. The authors of the paper under review study the effect of this duality on antiskeletal MV-algebras (for this definition see in the paper under review). Examples of antiskeletal MV-algebras are provided by free and by finitely generated projective MV-algebras. Every antiskeletal MV-algebra is indecomposable. The antiskeletal property is presented under subalgebras. It is proved that the class of antiskeletal MV-algebras is not definable in existential second-order logic, but is definable by a formula of monadic second-order logic. Algorithmic issues are considered in the final part of the paper. For background in MV-algebras see [\textit{R. Cignoli} et al., J. Pure Appl. Algebra 189, No. 1--3, 37--59 (2004; Zbl 1055.06004)] and [the reviewer, Advanced Łukasiewicz calculus and MV-algebras. Berlin: Springer (2011; Zbl 1235.03002)].
scientific article; zbMATH DE number 6996654