A determination principle for algebras of n-valued Łukasiewicz logic

The n-valued Łukasiewicz–Moisil algebras, MV-algebras and Post algebras are structures developed in connection to the algebra of the n-valued Łukasiewicz logic. In this paper, we obtain categorical equivalences which allow us to represent any such structure as an algebra of decreasing Boolean sequences of length n. Moreover any algebra L belonging to one of these classes is characterized using a sequence of n Boolean ideals I1,…,In⊆C(L), which are called the Boolean nuances of L. The type of L can be deduced from set-theoretical properties of the corresponding sequence of Boolean ideals. As an application, we prove that L is σ-complete if and only if the corresponding ideals are σ-closed.