Several algebraic structures (namely HW, BZMV , Stonean MV and MV∆ algebras) related to many valued logical systems are considered and their equivalence is proved. Four propositional calculi whose Lindenbaum– Tarski algebra corresponds to the four equivalent algebraic structures are axiomatized and their semantical completeness is given.

It is observed that a CL-algebra (Classical Linear Algebra) contains within it a number of MV-algebras (Many-valued Algebras). A necessary and sufficient condition is obtained when a CL-algebra as a whole reduces to an MV-algebra. All the embedded MValgebras are characterised. A special MV-algebra called the Stem of the CL-algebra is studied to some depth. © 1998 Elsevier Science Inc. All right...

An MV-convergence is a convergence on an MV-algebra which renders the operations continuous. We show that such convergences on a given MV-algebra A are exactly the restrictions of the bounded `-convergences on the abelian `-group in which A appears as the unit interval. Thus the theory of `-convergence and Cauchy structures transfers to MV-algebras. We outline the general theory, and then apply...

The aim of the present paper is to define the localisation of MValgebra of an MV-algebra A with respect to a topology F on A. In the last part of the paper it is proved that the maximal MV-algebra of quotients (defined in [6]) and the MV-algebra of fractions relative to an ∧−closed system (defined in [5]) are MV algebra of localisation. The concept of multiplier for distributive lattices was de...

There is given a construction of the entropy of a dynamical system on arbitrary MV-algebra M. If M is the MV-algebra of characteristic functions of a σ-algebra (isomorphic to the σ-algebra), then the construction leads to the Kolmogorov Sinaj entropy. If M is the MV-algebra (tribe) of fuzzy sets, then the construction coincides with the Maličký modification of the Kolmogorov Sinaj entropy for f...

The concept of an MV-algebra was introduced by Chang [4] as an algebraic basis for many-valued logic. It turned out that MV-algebras are a subclass of a more general class of effect algebras [7, 6]. Namely, MV-algebras are in one-to-one correspondence with lattice ordered effect algebras satisfying the Riesz decomposition property [2], the latter are called MV-effect algebras. In the study of c...

Flaminio and Montagna (2008) enlarged the language of MV-algebras by a unary operation σ, called internal state or a state operator, equationally defined so as to preserve the basic properties of a state in its usual meaning. The resulting class of MV-algebras is called state MV-algebras. Jenča (2007) and Vetterlein (2008), using different approaches, represented MV-algebras through the quotien...

It is known that any MV -algebra is a topological MV -algebra. For a locally finite MV -algebra A with some algebraic and topological conditions the product A× A becomes a compact Riemann surface (modulo conformal equivalence). Topologically, it is a torus.

An MV-pair is a pair (B, G), where B is a Boolean algebra and G is a subgroup of the automorphism group of B satisfying certain condition. Recently it was proved by one of the authors that for an MV-pair (B, G), ∼G is an effect-algebraic congruence and B/ ∼G is an MV-algebra. Moreover, every MV-algebra M can be represented by an MV-pair in this way. In this paper we show that one can define a s...

The paper provides a study of pseudo MV-algebras with square roots. We introduce different notions root on MV-algebra, and present their main properties. show that the class pseudo-MV-algebras roots is proper subvariety variety MV-algebras. Then, we define strict to classify found relationship between strongly atomless Finally, investigate representable symmetric MV-algebras, complete character...