Varieties of MV-algebras

Panti, Giovanni

doi:10.1080/11663081.1999.10510961

Cited by 25 publications

(19 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In [24] the authors show that there is a 1-1 correspondence between proper subvarieties of MV and reduced pairs of finite subsets of positive integers not both empty. Given a reduced pair (I, J ), we denote by V I,J its associated subvariety.…”

Section: Varieties and Quasivarieties Of Mv-algebrasmentioning

confidence: 98%

“…By abuse of notation we also let f (x) denote its associated MV-term. It follows from [24] that for every MV-chain A, if we assume without loss of generality that …”

Section: Least V-quasivarietiesmentioning

confidence: 99%

“…The existence is assured by the following general result of Universal Algebra (see for instance [4,18]). In the case of MV-algebras, since any subvariety of MV-algebras can be distinguished by an axiom in just one variable [24], the quasivariety generated by the free V-algebra over a one free generator is also the least V-quasivariety. [7].…”

Section: Least V-quasivarietiesmentioning

confidence: 99%

See 2 more Smart Citations

Least V-quasivarieties of MV-algebras

Gispert

2016

Fuzzy Sets and Systems

View full text Add to dashboard Cite

Section: Varieties and Quasivarieties Of Mv-algebrasmentioning

confidence: 98%

“…By abuse of notation we also let f (x) denote its associated MV-term. It follows from [24] that for every MV-chain A, if we assume without loss of generality that …”

Section: Least V-quasivarietiesmentioning

confidence: 99%

Section: Least V-quasivarietiesmentioning

confidence: 99%

See 1 more Smart Citation

Least V-quasivarieties of MV-algebras

Gispert

2016

Fuzzy Sets and Systems

View full text Add to dashboard Cite

“…An MV -algebra A = (A, 0, ¬, ⊕) is an abelian monoid (A, 0, ⊕) equipped with a unary operation ¬ such that ¬¬x = x, x ⊕¬0 = ¬0, and y ⊕¬(y ⊕¬x) = x ⊕¬(x ⊕y) [24]. We set 1 = ¬0 and x y = ¬(¬x ⊕¬y) [6].…”

Section: M-generated Free MV (C)-algebramentioning

confidence: 99%

Gödel spaces and perfect MV-algebras

Nola

Grigolia

2015

Journal of Applied Logic

View full text Add to dashboard Cite

The category of Gödel spaces GS (with strongly isotone maps as morphisms), which are dually equivalent to the category of Gödel algebras, is transferred by a contravariant functor H into the category MV(C)^G of MV-algebras generated by perfect MV-chains via the operators of direct products, subalgebras and direct limits. Conversely, the category MV(C)^G is transferred into the category GS by means of a contravariant functor P. Moreover, it is shown that the functor H is faithful, the functor P is full and the both functors are dense. The description of finite coproduct of algebras, which are isomorphic to Chang algebra, is given. Using duality a characterization of projective algebras in MV(C)^G is given

show abstract

“…Strengthening this result, a procedure is given in [88] to obtain for each pair I, J as above, an MV-term ν I,J (x) in the single variable x such that the defining equations of MV-algebras, together with the additional equation ν I,J (x) = 1 yield an axiomatization of V I,J .…”

Section: If the Rank Of A Is Infinite Then The Simple Mv-algebramentioning

confidence: 99%

MV-algebras: a variety for magnitudes with archimedean units

Gispert

Mundici

2005

Algebra univers.

View full text Add to dashboard Cite

Chang's MV-algebras, on the one hand, are the algebras of the infinite-valued Lukasiewicz calculus and, on the other hand, are categorically equivalent to abelian latticeordered groups with a distinguished strong unit, for short, unital -groups. The latter are a modern mathematization of the time-honored euclidean magnitudes with an archimedean unit. While for magnitudes the unit is no less important than the zero element, its archimedean property is not even definable in first-order logic. This gives added interest to the equivalent representation of unital -groups via the equational class of MV-algebras. In this paper we survey several applications of this equivalence, and various properties of the variety of MV-algebras. PrologueIn the last twenty years the number of papers devoted to Chang's MV-algebras [14] has been increasing so rapidly that, since the year 2000 the AMS Classification Index contains the special item 06D35 for MV-algebras. To quote just a handful of books, the monograph [25] by Cignoli et al., is entirely devoted to MValgebras, Hajek's monograph [56] and Gottwald's book [54] devote ample space to these algebras. As shown in [37] and [94], MV-algebras also provide an interesting example of "quantum structures". The Handbook of Measure Theory [89] includes several chapters on MV-algebraic measure theory. As the Lindenbaum algebras of Lukasiewicz infinite-valued logic, MV-algebras are also considered in many surveys, e.g., [21,68,87]. In this paper we will present several main topics in the theory of MV-algebras which are of greater potential interest for the universal algebraist. We apologize to authors and readers for all omissions, mainly due to lack of space.

show abstract

Varieties of MV-algebras

Cited by 25 publications

References 8 publications

Least V-quasivarieties of MV-algebras

Least V-quasivarieties of MV-algebras

Gödel spaces and perfect MV-algebras

MV-algebras: a variety for magnitudes with archimedean units

Contact Info

Product

Resources

About