Results for 'MV‐algebras'

997 found
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  1.  20
    The Dual Adjunction Between MV-Algebras and Tychonoff Spaces.Vincenzo Marra & Luca Spada - 2012 - Studia Logica 100 (1-2):253-278.
    We offer a proof of the duality theorem for finitely presented MV-algebras and rational polyhedra, a folklore and yet fundamental result. Our approach develops first a general dual adjunction between MV-algebras and subspaces of Tychonoff cubes, endowed with the transformations that are definable in the language of MV-algebras. We then show that this dual adjunction restricts to a duality between semisimple MV-algebras and closed subspaces of Tychonoff cubes. The duality theorem for finitely presented objects is obtained by a further specialisation. (...)
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  2.  40
    On the Equivalence Between MV-Algebras and L-Groups with Strong Unit.Eduardo J. Dubuc & Y. A. Poveda - 2015 - Studia Logica 103 (4):807-814.
    In “A new proof of the completeness of the Lukasiewicz axioms” Chang proved that any totally ordered MV-algebra A was isomorphic to the segment \}\) of a totally ordered l-group with strong unit A *. This was done by the simple intuitive idea of putting denumerable copies of A on top of each other. Moreover, he also show that any such group G can be recovered from its segment since \^*}\), establishing an equivalence of categories. In “Interpretation of AF C (...)
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  3.  34
    Finitely Generated Free MV-Algebras and Their Automorphism Groups.Antonio Di Nola, Revaz Grigolia & Giovanni Panti - 1998 - Studia Logica 61 (1):65-78.
    The MV-algebra S m w is obtained from the (m+1)-valued ukasiewicz chain by adding infinitesimals, in the same way as Chang's algebra is obtained from the two-valued chain. These algebras were introduced by Komori in his study of varieties of MV-algebras. In this paper we describe the finitely generated totally ordered algebras in the variety MV m w generated by S m w . This yields an easy description of the free MV m w -algebras over one generator. We characterize (...)
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  4.  25
    An Elementary Presentation of the Equivalence Between MV-Algebras and L-Groups with Strong Unit.Roberto Cignoli & Daniele Mundici - 1998 - Studia Logica 61 (1):49-64.
    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.
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  5.  28
    The Lattice of Subvarieties of $${\Sqrt{\Prime}}$$ Quasi-MV Algebras.T. Kowalski, F. Paoli, R. Giuntini & A. Ledda - 2010 - Studia Logica 95 (1-2):37-61.
    In the present paper we continue the investigation of the lattice of subvarieties of the variety of ${\sqrt{\prime}}$ quasi-MV algebras, already started in [6]. Beside some general results on the structure of such a lattice, the main contribution of this work is the solution of a long-standing open problem concerning these algebras: namely, we show that the variety generated by the standard disk algebra D r is not finitely based, and we provide an infinite equational basis for the same variety.
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  6.  9
    Monadic MV-Algebras Are Equivalent to Monadic ℓ-Groups with Strong Unit.C. Cimadamore & J. P. Díaz Varela - 2011 - Studia Logica 98 (1-2):175-201.
    In this paper we extend Mundici’s functor Γ to the category of monadic MV-algebras. More precisely, we define monadic ℓ -groups and we establish a natural equivalence between the category of monadic MV-algebras and the category of monadic ℓ -groups with strong unit. Some applications are given thereof.
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  7.  32
    On Certain Quasivarieties of Quasi-MV Algebras.A. Ledda, T. Kowalski & F. Paoli - 2011 - Studia Logica 98 (1-2):149-174.
    Quasi-MV algebras are generalisations of MV algebras arising in quantum computational logic. Although a reasonably complete description of the lattice of subvarieties of quasi-MV algebras has already been provided, the problem of extending this description to the setting of quasivarieties has so far remained open. Given its apparent logical repercussions, we tackle the issue in the present paper. We especially focus on quasivarieties whose generators either are subalgebras of the standard square quasi-MV algebra S , or can be obtained therefrom (...)
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  8.  21
    The Intimate Relationship Between the McNaughton and the Chinese Remainder Theorems for MV-Algebras.Eduardo J. Dubuc & Yuri Poveda - 2013 - Studia Logica 101 (3):483-485.
    We show the intimate relationship between McNaughton Theorem and the Chinese Remaindner Theorem for MV-algebras. We develop a very short and simple proof of McNaughton Theorem. The arguing is elementary and right out of the definitions. We exhibit the theorem as just an instance of the Chinese theorem. Since the variety of MV-algebras is arithmetic, the Chinese theorem holds for MV-algebras. However, to make this paper self-contained and entirely elementary, we include a simple proof of this theorem inspired in Ferraioli (...)
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  9.  9
    A Preliminary Study of MV-Algebras with Two Quantifiers Which Commute.Aldo Figallo Orellano - 2016 - Studia Logica 104 (5):931-956.
    In this paper we investigate the class of MV-algebras equipped with two quantifiers which commute as a natural generalization of diagonal-free two-dimensional cylindric algebras. In the 40s, Tarski first introduced cylindric algebras in order to provide an algebraic apparatus for the study of classical predicate calculus. The diagonal–free two-dimensional cylindric algebras are special cylindric algebras. The treatment here of MV-algebras is done in terms of implication and negation. This allows us to simplify some results due to Di Nola and Grigolia (...)
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  10.  11
    A Characterization of MV-Algebras Free Over Finite Distributive Lattices.Vincenzo Marra - 2008 - Archive for Mathematical Logic 47 (3):263-276.
    Mundici has recently established a characterization of free finitely generated MV-algebras similar in spirit to the representation of the free Boolean algebra with a countably infinite set of free generators as any Boolean algebra that is countable and atomless. No reference to universal properties is made in either theorem. Our main result is an extension of Mundici’s theorem to the whole class of MV-algebras that are free over some finite distributive lattice.
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  11.  9
    Boolean Skeletons of MV-Algebras and ℓ-Groups.Roberto Cignoli - 2011 - Studia Logica 98 (1-2):141-147.
    Let Γ be Mundici’s functor from the category $${\mathcal{LG}}$$ whose objects are the lattice-ordered abelian groups ( ℓ -groups for short) with a distinguished strong order unit and the morphisms are the unital homomorphisms, onto the category $${\mathcal{MV}}$$ of MV-algebras and homomorphisms. It is shown that for each strong order unit u of an ℓ -group G , the Boolean skeleton of the MV-algebra Γ ( G , u ) is isomorphic to the Boolean algebra of factor congruences of G.
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  12.  10
    Monadic MV-Algebras Are Equivalent to Monadic?-Groups with Strong Unit.C. Cimadamore & J. P. D.?az Varela - 2011 - Studia Logica 98 (1-2):175-201.
    In this paper we extend Mundici's functor? to the category of monadic MV- algebras. More precisely, we define monadic?- groups and we establish a natural equivalence between the category of monadic MV- algebras and the category of monadic?- groups with strong unit. Some applications are given thereof.
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  13.  21
    Representation and Extension of States on MV-Algebras.TomአKroupa - 2005 - Archive for Mathematical Logic 45 (4):381-392.
    MV-algebras stand for the many-valued Łukasiewicz logic the same as Boolean algebras for the classical logic. States on MV-algebras were first mentioned [20] in probability theory and later also introduced in effort to capture a notion of `an average truth-value of proposition' [15] in Łukasiewicz many-valued logic. In the presented paper, an integral representation theorem for finitely-additive states on semisimple MV-algebra will be proven. Further, we shall prove extension theorems concerning states defined on sub-MV-algebras and normal partitions of unity generalizing (...)
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  14.  13
    Representations of MV-Algebras by Sheaves.Anna R. Ferraioli & Ada Lettieri - 2011 - Mathematical Logic Quarterly 57 (1):27-43.
    In this paper, inspired by methods of Bigard, Keimel, and Wolfenstein , we develop an approach to sheaf representations of MV-algebras which combines two techniques for the representation of MV-algebras devised by Filipoiu and Georgescu and by Dubuc and Poveda . Following Davey approach , we use a subdirect representation of MV-algebras that is based on local MV-algebras. This allowed us to obtain: a representation of any MV-algebras as MV-algebra of all global sections of a sheaf of local MV-algebras on (...)
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  15.  17
    Hyper MV -Ideals in Hyper MV -Algebras.Lida Torkzadeh & Afsaneh Ahadpanah - 2010 - Mathematical Logic Quarterly 56 (1):51-62.
    In this paper we define the hyper operations ⊗, ∨ and ∧ on a hyper MV -algebra and we obtain some related results. After that by considering the notions ofhyper MV -ideals and weak hyper MV -ideals, we prove some theorems. Then we determine relationships between hyper MV -ideals in a hyper MV -algebra and hyper K -ideals in a hyper K -algebra . Finally we give a characterization of hyper MV -algebras of order 3 or 4 based on the (...)
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  16.  10
    On the Category of Hyper MV‐Algebras.Shokoofeh Ghorbani, Esfandiar Eslami & Abbas Hasankhani - 2009 - Mathematical Logic Quarterly 55 (1):21-30.
    In this paper we study the category of hyper MV-algebras and we prove that it has a terminal object and a coequalizer. We show that Jia's construction can be modified to provide a free hyper MV-algebra by a set. We use this to show that in the category of hyper MV-algebras the monomorphisms are exactly the one-to-one homomorphisms.
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  17.  38
    A Discrete Representation of Free MV-Algebras.Antonio Di Nola, Revaz Grigolia & Luca Spada - 2010 - Mathematical Logic Quarterly 56 (3):279-288.
    We prove that the m -generated free MV-algebra is isomorphic to a quotient of the disjoint union of all the m -generated free MV-algebras. Such a quotient can be seen as the direct limit of a system consisting of all free MV-algebras and special maps between them as morphisms.
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  18.  5
    Hyper-Archimedean BL-Algebras Are MV-Algebras.Esko Turunen - 2007 - Mathematical Logic Quarterly 53 (2):170-175.
    Generalizations of Boolean elements of a BL-algebra L are studied. By utilizing the MV-center MV(L) of L, it is reproved that an element x L is Boolean iff x x * = 1. L is called semi-Boolean if for all x L, x * is Boolean. An MV-algebra L is semi-Boolean iff L is a Boolean algebra. A BL-algebra L is semi-Boolean iff L is an SBL-algebra. A BL-algebra L is called hyper-Archimedean if for all x L, xn is Boolean (...)
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  19.  26
    Representation of MV-Algebras by Regular Ultrapowers of [0, 1].Antonio Di Nola, Giacomo Lenzi & Luca Spada - 2010 - Archive for Mathematical Logic 49 (4):491-500.
    We present a uniform version of Di Nola Theorem, this enables to embed all MV-algebras of a bounded cardinality in an algebra of functions with values in a single non-standard ultrapower of the real interval [0,1]. This result also implies the existence, for any cardinal α, of a single MV-algebra in which all infinite MV-algebras of cardinality at most α embed. Recasting the above construction with iterated ultrapowers, we show how to construct such an algebra of values in a definable (...)
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  20.  18
    A Common Generalization for MV-Algebras and Łukasiewicz–Moisil Algebras.George Georgescu & Andrei Popescu - 2006 - Archive for Mathematical Logic 45 (8):947-981.
    We introduce the notion of n-nuanced MV-algebra by performing a Łukasiewicz–Moisil nuancing construction on top of MV-algebras. These structures extend both MV-algebras and Łukasiewicz–Moisil algebras, thus unifying two important types of structures in the algebra of logic. On a logical level, n-nuanced MV-algebras amalgamate two distinct approaches to many valuedness: that of the infinitely valued Łukasiewicz logic, more related in spirit to the fuzzy approach, and that of Moisil n-nuanced logic, which is more concerned with nuances of truth rather than (...)
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  21.  16
    Cyclic Elements in MV‐Algebras and Post Algebras.Antoni Torrens - 1994 - Mathematical Logic Quarterly 40 (4):431-444.
    In this paper we characterize the MV-algebras containing as subalgebras Post algebras of finitely many orders. For this we study cyclic elements in MV-algebras which are the generators of the fundamental chain of the Post algebras.
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  22.  14
    On Vaught’s Conjecture and Finitely Valued MV Algebras.Antonio Di Nola & Giacomo Lenzi - 2012 - Mathematical Logic Quarterly 58 (3):139-152.
    We show that the complete first order theory of an MV algebra has equation image countable models unless the MV algebra is finitely valued. So, Vaught's Conjecture holds for all MV algebras except, possibly, for finitely valued ones. Additionally, we show that the complete theories of finitely valued MV algebras are equation image and that all ω-categorical complete theories of MV algebras are finitely axiomatizable and decidable. As a final result we prove that the free algebra on countably many generators (...)
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  23.  9
    Conservative Extension of Polyadic MV-Algebras to Polyadic Pavelka Algebras.Dumitru Daniel Drăgulici - 2006 - Archive for Mathematical Logic 45 (5):601-613.
    In this paper we prove polyadic counterparts of the Hájek, Paris and Shepherdson's conservative extension theorems of Łukasiewicz predicate logic to rational Pavelka predicate logic. We also discuss the algebraic correspondents of the provability and truth degree for polyadic MV-algebras and prove a representation theorem similar to the one for polyadic Pavelka algebras.
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  24.  8
    Fuzzy Topology Representation for MV‐Algebras.Jialu Zhang & Quanfa Chen - 2009 - Mathematical Logic Quarterly 55 (3):259-270.
    Let M be an MV-algebra and ΩM be the set of all σ -valuations from M into the MV-unit interval. This paper focuses on the characterization of MV-algebras using σ -valuations of MV-algebras and proves that a σ -complete MV-algebra is σ -regular, which means that a ≤ b if and only if v ≤ v for any v ∈ ΩM. Then one can introduce in a natural way a fuzzy topology δ on ΩM. The representation theorem forMV-algebras is established (...)
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  25.  14
    On Monadic MV-Algebras.Antonio Di Nola & Revaz Grigolia - 2004 - Annals of Pure and Applied Logic 128 (1-3):125-139.
    We define and study monadic MV-algebras as pairs of MV-algebras one of which is a special case of relatively complete subalgebra named m-relatively complete. An m-relatively complete subalgebra determines a unique monadic operator. A necessary and sufficient condition is given for a subalgebra to be m-relatively complete. A description of the free cyclic monadic MV-algebra is also given.
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  26.  72
    MV-Algebras and Quantum Computation.Antonio Ledda, Martinvaldo Konig, Francesco Paoli & Roberto Giuntini - 2006 - Studia Logica 82 (2):245-270.
    We introduce a generalization of MV algebras motivated by the investigations into the structure of quantum logical gates. After laying down the foundations of the structure theory for such quasi-MV algebras, we show that every quasi-MV algebra is embeddable into the direct product of an MV algebra and a “flat” quasi-MV algebra, and prove a completeness result w.r.t. a standard quasi-MV algebra over the complex numbers.
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  27.  3
    Representation Theory of MV-Algebras.Eduardo J. Dubuc & Yuri A. Poveda - 2010 - Annals of Pure and Applied Logic 161 (8):1024-1046.
    In this paper we develop a general representation theory for MV-algebras. We furnish the appropriate categorical background to study this problem. Our guide line is the theory of classifying topoi of coherent extensions of universal algebra theories. Our main result corresponds, in the case of MV-algebras and MV-chains, to the representation of commutative rings with unit as rings of global sections of sheaves of local rings. We prove that any MV-algebra is isomorphic to the MV-algebra of all global sections of (...)
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  28.  59
    Duality, Projectivity, and Unification in Łukasiewicz Logic and MV-Algebras.Vincenzo Marra & Luca Spada - 2013 - Annals of Pure and Applied Logic 164 (3):192-210.
    We prove that the unification type of Łukasiewicz logic and of its equivalent algebraic semantics, the variety of MV-algebras, is nullary. The proof rests upon Ghilardiʼs algebraic characterisation of unification types in terms of projective objects, recent progress by Cabrer and Mundici in the investigation of projective MV-algebras, the categorical duality between finitely presented MV-algebras and rational polyhedra, and, finally, a homotopy-theoretic argument that exploits lifts of continuous maps to the universal covering space of the circle. We discuss the background (...)
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  29.  24
    State-Morphism MV-Algebras.Antonio Di Nola & Anatolij Dvurečenskij - 2009 - Annals of Pure and Applied Logic 161 (2):161-173.
    We present a stronger variation of state MV-algebras, recently presented by T. Flaminio and F. Montagna, which we call state-morphism MV-algebras. Such structures are MV-algebras with an internal notion, a state-morphism operator. We describe the categorical equivalences of such state MV-algebras with the category of unital Abelian ℓ-groups with a fixed state operator and present their basic properties. In addition, in contrast to state MV-algebras, we are able to describe all subdirectly irreducible state-morphism MV-algebras.
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  30.  23
    States on Pseudo MV-Algebras.Anatolij Dvurečenskij - 2001 - Studia Logica 68 (3):301-327.
    Pseudo MV-algebras are a non-commutative extension of MV-algebras introduced recently by Georgescu and Iorgulescu. We introduce states (finitely additive probability measures) on pseudo MV-algebras. We show that extremal states correspond to normal maximal ideals. We give an example in that, in contrast to classical MV-algebras introduced by Chang, states can fail on pseudo MV-algebras. We prove that representable and normal-valued pseudo MV-algebras admit at least one state.
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  31.  24
    Perfect MV-Algebras Are Categorically Equivalent to Abelianl-Groups.Antonio Di Nola & Ada Lettieri - 1994 - Studia Logica 53 (3):417-432.
    In this paper we prove that the category of abelianl-groups is equivalent to the category of perfect MV-algebras. Furthermore, we give a finite equational axiomatization of the variety generated by perfect MV-algebras.
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  32.  32
    Erratum to “Representation Theory of MV-Algebras” [Ann. Pure Appl. Logic 161 ].Eduardo J. Dubuc - 2012 - Annals of Pure and Applied Logic 163 (9):1358.
    In this paper we develop a general representation theory for MV-algebras. We furnish the appropriate categorical background to study this problem. Our guide line is the theory of classifying topoi of coherent extensions of universal algebra theories. Our main result corresponds, in the case of MV-algebras and MV-chains, to the representation of commutative rings with unit as rings of global sections of sheaves of local rings. We prove that any MV-algebra is isomorphic to the MV-algebra of all global sections of (...)
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  33.  70
    Expanding Quasi-MV Algebras by a Quantum Operator.Roberto Giuntini, Antonio Ledda & Francesco Paoli - 2007 - Studia Logica 87 (1):99-128.
    We investigate an expansion of quasi-MV algebras ([10]) by a genuine quantum unary operator. The variety of such quasi-MV algebras has a subquasivariety whose members—called cartesian—can be obtained in an appropriate way out of MV algebras. After showing that cartesian . quasi-MV algebras generate ,we prove a standard completeness theorem for w.r.t. an algebra over the complex numbers.
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  34.  7
    Convex MV-Algebras: Many-Valued Logics Meet Decision Theory.T. Flaminio, H. Hosni & S. Lapenta - 2018 - Studia Logica 106 (5):913-945.
    This paper introduces a logical analysis of convex combinations within the framework of Łukasiewicz real-valued logic. This provides a natural link between the fields of many-valued logics and decision theory under uncertainty, where the notion of convexity plays a central role. We set out to explore such a link by defining convex operators on MV-algebras, which are the equivalent algebraic semantics of Łukasiewicz logic. This gives us a formal language to reason about the expected value of bounded random variables. As (...)
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  35.  68
    Varieties of MV-Algebras.Giovanni Panti - 1999 - Journal of Applied Non-Classical Logics 9 (1):141-157.
    ABSTRACT We characterize, for every subvariety V of the variety of all MV- algebras, the free objects in V. We use our results to compute coproducts in V and to provide simple single-axiom axiomatizations of all many-valued logics extending the Lukasiewicz one.
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  36. On Some Properties of Quasi-MV Algebras and $\Sqrt{^{\Prime }}$ Quasi-MV Algebras.Francesco Paoli, Antonio Ledda, Roberto Giuntini & Hector Freytes - 2009 - Reports on Mathematical Logic:31-63.
    We investigate some properties of two varieties of algebras arising from quantum computation - quasi-MV algebras and $\sqrt{^{\prime }}$ quasi-MV algebras - first introduced in \cite{Ledda et al. 2006}, \cite{Giuntini et al. 200+} and tightly connected with fuzzy logic. We establish the finite model property and the congruence extension property for both varieties; we characterize the quasi-MV reducts and subreducts of $\sqrt{^{\prime }}$ quasi-MV algebras; we give a representation of semisimple $\sqrt{^{\prime }}$ quasi-MV algebras in terms of algebras of functions; (...)
     
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  37.  36
    States on Polyadic MV-Algebras.George Georgescu - 2010 - Studia Logica 94 (2):231-243.
    This paper is a contribution to the algebraic logic of probabilistic models of Łukasiewicz predicate logic. We study the MV-states defined on polyadic MV-algebras and prove an algebraic many-valued version of Gaifman’s completeness theorem.
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  38.  4
    Yosida Type Representation for Perfect MV‐Algebras.Lawrence P. Belluce & Antonio Di Nola - 1996 - Mathematical Logic Quarterly 42 (1):551-563.
    In [9] Mundici introduced a categorical equivalence Γ between the category of MV-algebras and the category of abelian [MATHEMATICAL SCRIPT SMALL L]-groups with strong unit. Using Mundici's functor Γ, in [8] the authors established an equivalence between the category of perfect MV-algebras and the category of abelian [MATHEMATICAL SCRIPT SMALL L]-groups. Aim of the present paper is to use the above functors to provide Yosida like representations of a large class of MV-algebras.
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  39.  7
    MV*—Algebras.Renato Lewin, Marta Sagastume & Pedro Massey - 2004 - Logic Journal of the IGPL 12 (6):461-483.
    In this paper we make an algebraic study of the variety of MV*-algebras introduced by C. C. Chang as an algebraic counterpart for a logic with positive and negative truth values.We build the algebraic theory of MV*-algebras within its own limits using a concept of ideal and of prime ideal that are very naturally related to the corresponding concepts in l-groups. The main results are a subdirect representation theorem, a completeness theorem, a study of simple and semisimple algebras, and a (...)
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  40.  45
    Quantum MV Algebras.Roberto Giuntini - 1996 - Studia Logica 56 (3):393 - 417.
    We introduce the notion of quantum MV algebra (QMV algebra) as a generalization of MV algebras and we show that the class of all effects of any Hilbert space gives rise to an example of such a structure. We investigate some properties of QMV algebras and we prove that QMV algebras represent non-idempotent extensions of orthomodular lattices.
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  41.  9
    The Lattice of Subvarieties of √′ Quasi-MV Algebras.T. Kowalski, F. Paoli, R. Giuntini & A. Ledda - 2010 - Studia Logica 95 (1-2):37 - 61.
    In the present paper we continue the investigation of the lattice of subvarieties of the variety of √′ P quasi-MV algebras, already started in [6]. Beside some general results on the structure of such a lattice, the main contribution of this work is the solution of a long-standing open problem concerning these algebras: namely, we show that the variety generated by the standard disk algebra D r is not finitely based, and we provide an infinite equational basis for the same (...)
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  42.  43
    The Variety of Lattice Effect Algebras Generated by MV-Algebras and the Horizontal Sum of Two 3-Element Chains.Radomír Halaš - 2008 - Studia Logica 89 (1):19-35.
    It has been recently shown [4] that the lattice effect algebras can be treated as a subvariety of the variety of so-called basic algebras. The open problem whether all subdirectly irreducible distributive lattice effect algebras are just subdirectly irreducible MV-chains and the horizontal sum of two 3-element chains is in the paper transferred into a more tractable one. We prove that modulo distributive lattice effect algebras, the variety generated by MV-algebras and is definable by three simple identities and the problem (...)
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  43.  59
    A Common Abstraction of MV-Algebras and Abelian L-Groups.Francesco Paoli - 2000 - Studia Logica 65 (3):355-366.
    We investigate the class of strongly distributive pregroups, a common abstraction of MV-algebras and Abelian l-groups which was introduced by E.Casari. The main result of the paper is a representation theorem which yields both Chang's representation of MV-algebras and Clifford's representation of Abelian l-groups as immediate corollaries.
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  44.  5
    MVW-Rigs and Product MV-Algebras.Alejandro Estrada & Yuri A. Poveda - 2018 - Journal of Applied Non-Classical Logics 29 (1):78-96.
    ABSTRACTWe introduce the variety of Many-Valued-Weak rigs. We provide an axiomatisation and establish, in this context, basic properties about ideals, homomorphisms, quotients and radicals. This new class contains the class of product MV-algebras presented by Di Nola and Dvurečenskij in 2001 and by Montagna in 2005. The main result is the compactness of the prime spectrum of this new class, endowed with the co-Zariski topology as defined by Dubuc and Poveda in 2010.
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  45.  31
    Algebraically Closed MV-Algebras and Their Sheaf Representation.Antonio Di Nola, Anna R. Ferraioli & Giacomo Lenzi - 2013 - Annals of Pure and Applied Logic 164 (3):349-355.
    In this paper we first provide a new axiomatization of algebraically closed MV-algebras based on McNaughtonʼs Theorem. Then we turn to sheaves, and we represent algebraically closed MV-algebras as algebras of global sections of sheaves, where the stalks are divisible MV-chains and the base space is Stonean.
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  46.  13
    Perfect MV-Algebras and L-Rings.Lawrence P. Belluce, Antonio Di Nola & George Georgescu - 1999 - Journal of Applied Non-Classical Logics 9 (1):159-172.
    ABSTRACT In this paper we shall prove that l-rings are categorally equivalent to the MV*-algebras, a subcategory of perfect MV-algebras. We shall use this equivalence in order to characterize l-rings as quotients of certain semirings of matrices over MV*-algebras. We shall establish a relation between l-ideals in l-rings and some ideals in MV*-algebras. This edlows us to study the MV* f-algebras, a subclass of the MV*-algebras corresponding to the f-rings.
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  47.  19
    Quasivarieties Generated by Simple MV-Algebras.Joan Gispert & Antoni Torrens - 1998 - Studia Logica 61 (1):79-99.
    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.
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  48.  4
    Fuzzy Topology Representation for MV-Algebras.Jialu Zhang & Quanfa Chen - 2009 - Mathematical Logic Quarterly 55 (3):259-270.
    Let M be an MV-algebra and ΩM be the set of all σ -valuations from M into the MV-unit interval. This paper focuses on the characterization of MV-algebras using σ -valuations of MV-algebras and proves that a σ -complete MV-algebra is σ -regular, which means that a ≤ b if and only if v ≤ v for any v ∈ ΩM. Then one can introduce in a natural way a fuzzy topology δ on ΩM. The representation theorem forMV-algebras is established (...)
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  49.  4
    Varying Interpolation and Amalgamation in Polyadic MV-Algebras.Tarek Sayed Ahmed - 2015 - Journal of Applied Non-Classical Logics 25 (2):140-192.
    We prove several interpolation theorems for many-valued infinitary logic with quantifiers by studying expansions of MV-algebras in the spirit of polyadic and cylindric algebras. We prove for various reducts of polyadic MV-algebras of infinite dimensions that if is the free algebra in the given signature,, is in the subalgebra of generated by, is in the subalgebra of generated by and, then there exists an interpolant in the subalgebra generated by and such that. We call this a varying interpolation property because (...)
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  50. Duality Theory and Skeleta for Semisimple MV-Algebras.Antonio Di Nola & Giacomo Lenzi - 2018 - Studia Logica 106 (6):1239-1260.
    We start from Marra–Spada duality between semisimple MV-algebras and Tychonoff spaces, and we consider the particular cases when the \-skeleta of the MV-algebras are restricted in some way. In particular we consider antiskeletal MV-algebras, that is, the ones whose \-skeleton is trivial.
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