Quasivarieties Generated by Simple MV-algebras

In this paper we show that the quasivariety generated by an infinite simple MV-algebra only depends on the rationals which it contains. We extend this property to arbitrary families of simple MV-algebras.     

An Elementary Presentation of the Equivalence Between MV-algebras and l-groups With Strong Unit

Aim of this paper is to provide a self-contained presentation of the natural equivalence between MV-algebras and lattice-ordered abelian groups with strong unit.     

Maximal Subalgebras of MVn-algebras. A Proof of a Conjecture of A. Monteiro

For each integer n ≥ 2, MV_n denotes the variety of MV-algebras generated by the MV-chain with n elements. Algebras in MV_n are represented as continuous functions from a Boolean space into a n-element chain equipped with the discrete topology. Using these representations, maximal subalgebras of algebras in MV_n are characterized, and it is shown that proper subalgebras are intersection of maximal subalgebras. When A ∈ MV₃, the mentioned characterization of maximal subalgebras of A can be given in terms of prime filters of the underlying lattice of A, in the form that was conjectured by A. Monteiro. Mathematics Subject Classification (2000): 06D30, 06D35, 03G20, 03B50, 08A30. Presented by Daniele Mundici     

A Duality for the Algebras of a Łukasiewicz <Emphasis Type="Italic">n</Emphasis> + 1-valued Modal System

In this paper, we develop a duality for the varieties of a Łukasiewicz n + 1-valued modal system. This duality is an extension of Stone duality for modal algebras. Some logical consequences (such as completeness results, correspondence theory...) are then derived and we propose some ideas for future research. Presented by Daniele Mundici