Finiteness and duality in MV-algebras theory (Q2784592)

The authors investigate some finiteness conditions for MV-algebras. Firstly, they define a particular type of MV-algebras by using words constructed by means of a finite alphabet; such algebras are called MV-algebras of words. It is proved that each finite MV-algebra is isomorphic to some MV-algebra of words. Secondly, by using Priestley spaces, the authors describe a duality between finite MV-algebras and finite posets. Thirdly, the authors prove a series of results on the category \(\mathbf{q}\mathbb{FC}\) of quasi-finite \(\text{MV}(C)\) algebras; the class \(\mathbf{qF}\) of such algebras is defined by the following conditions: 1) \(\mathbf{qF}\) contains every finitely generated perfect chain; 2) \(\mathbf{qF}\) is the smallest class containing every finitely generated perfect chain and closed under finite products, homomorphic images and subalgebras.NEWLINENEWLINEFor the entire collection see [Zbl 0970.00009].