Abelian \(\ell\)-groups with strong unit and perfect MV-algebras
In his paper [J. Funct. Anal. 65, 15--63 (1986; Zbl 0597.46059)], the present reviewer established a categorical equivalence \(\Gamma\) between MV-algebras and unital lattice-ordered abelian groups. MV-algebras stand to Boolean algebras as infinite-valued Łukasiewicz logic stands to Boolean logic. They were introduced in 1958 by C. C. Chang to prove the completeness theorem for Łukasiewicz infinite-valued propositional logic. By definition, perfect MV-algebras are generated by their radical. They were more recently introduced by Belluce, Di Nola and B. Gerla, and shown to be categorically equivalent to lattice-ordered abelian groups. In the present paper, the authors describe the \(\Gamma\)-correspondents of perfect MV-algebras and of local MV-algebras with finite rank.
scientific article; zbMATH DE number 5547257
scientific article