An MV-algebraic invariant for boolean algebras with a finite-orbit automorphism

Rok, strany: 2003, 23 - 43

We classify boolean algebras equipped with a distinguished automorphism having no infinite orbit. For any object in this category, its corresponding invariant is a locally finite MV-algebra—the colimit (or, in universal algebra terms, the direct limit) of finite MV-algebras. Locally finite MV-algebras are an infinite-valued generalization of boolean algebras. All locally finite MV-algebras arise in this classification. However, this invariant does not determine an equivalence of categories. We shall use multisets as an intermediate invariant, and then apply the duality between multisets and locally finite MV-algebras. The latter was recently established by the present authors, and is an extension of Stone's duality between boolean spaces and boolean algebras. Our results show that an important class of MV-algebras is essentially the same as the class of boolean algebras equipped with a finite-orbit automorphism. Given the role of MV-algebras in infinite-valued logic, our results suggest that logical multi-valuedness can be developed within the framework of classical logic.

ISO 690:

Cignoli, R., Dubuc, E., Mundici, D. 2003. An MV-algebraic invariant for boolean algebras with a finite-orbit automorphism. In Tatra Mountains Mathematical Publications, vol. 27, no.3, pp. 23-43. 1210-3195.

APA:

Cignoli, R., Dubuc, E., Mundici, D. (2003). An MV-algebraic invariant for boolean algebras with a finite-orbit automorphism. Tatra Mountains Mathematical Publications, 27(3), 23-43. 1210-3195.