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In this paper we investigate a class of MV-algebras built up by fixing a Boolean algebra, one of its maximal ideals and an
In this paper we use tools from the theory of MV-algebras and MV-algebraic states to study infinitesimal perturbations of classical (i.e. Boolean) events and their non-Archimedean probability. In particular we deal with a class of MV-algebras which can be roughly defined by attaching a cloud of infinitesimals to every element of a finite Boolean al...
The rotation of the product t-norm provides the tool to show that Łukasiewicz logic cannot be axiomatised as an extension of MTL by means of any set of axioms with at most one variable. As a corollary, also BL cannot be axiomatised from MTL by means of single-variable axioms.
In this paper, we give a further development of ideal theory for MV-semirings started in . Given an MV-couple (A, S), we have that Spec(S) and coSpec(A) are homeomorphic, but in general this doesn't happen if we consider Spec(A). So we are interested in what happens considering the frame of open subsets of these topological spaces. We obtain the...
In this paper, we give a further developmentment of ideal theory for MV-semirings started in [?]. Given an MV-couple (A, S), show Spec(S) and coSpec(A) are homeomorphic; in general this doesn't happen. We are interested in what happens considering the frame of open subsets of these topological spaces. We obtain the following results: i) the set of...
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.
In this paper we show that the classes of MV-algebras and MV-semirings are isomorphic as categories. This approach allows one to keep the inspiration and use new tools from semiring theory to analyze the class of MV-algebras. We present a representation of MV-semirings by MV-semirings of continuous sections in a sheaf of commutative semirings whose...
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...