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Embeddings of totally ordered MV-algebras of bounded cardinality

Piotr J. Wojciechowski (2009)

Fundamenta Mathematicae

For a given cardinal number 𝔞, we construct a totally ordered MV-algebra M(𝔞) having the property that every totally ordered MV-algebra of cardinality at most 𝔞 embeds into M(𝔞). In case 𝔞 = ℵ₀, the algebra M(𝔞) is the first known MV-algebra with respect to which the deductive system for the infinitely-valued Łukasiewicz's propositional logic is strongly complete.

Entropy on effect algebras with Riesz decomposition property II: MV-algebras

Antonio Di Nola, Anatolij Dvurečenskij, Marek Hyčko, Corrado Manara (2005)

Kybernetika

We study the entropy mainly on special effect algebras with (RDP), namely on tribes of fuzzy sets and sigma-complete MV-algebras. We generalize results from [RiMu] and [RiNe] which were known only for special tribes.

Entropy on effect algebras with the Riesz decomposition property I: Basic properties

Antonio Di Nola, Anatolij Dvurečenskij, Marek Hyčko, Corrado Manara (2005)

Kybernetika

We define the entropy, lower and upper entropy, and the conditional entropy of a dynamical system consisting of an effect algebra with the Riesz decomposition property, a state, and a transformation. Such effect algebras allow many refinements of two partitions. We present the basic properties of these entropies and these notions are illustrated by many examples. Entropy on MV-algebras is postponed to Part II.

Epimorphisms between finite MV-algebras

Aldo V. Figallo, Marina B. Lattanzi (2017)

Mathematica Bohemica

MV-algebras were introduced by Chang to prove the completeness of the infinite-valued Łukasiewicz propositional calculus. Recently, algebraic theory of MV-algebras has been intensively studied. Wajsberg algebras are just a reformulation of Chang MV-algebras where implication is used instead of disjunction. Using these equivalence, in this paper we provide conditions for the existence of an epimorphism between two finite MV-algebras $A$ and $B$ . Specifically, we define the mv-functions with domain in...

Every uniformly Archimedean atomic MV-effect algebra is sharply dominating

Vladimír Olejček (2010)

Kybernetika

Following the study of sharp domination in effect algebras, in particular, in atomic Archimedean MV-effect algebras it is proved that if an atomic MV-effect algebra is uniformly Archimedean then it is sharply dominating.

Extensional subobjects in categories of $Ω$ -fuzzy sets

Jiří Močkoř (2007)

Czechoslovak Mathematical Journal

Two categories $𝕊𝕖𝕥 (Ω)$ and $𝕊𝕖𝕥𝔽 (Ω)$ of fuzzy sets over an $M V$ -algebra $Ω$ are investigated. Full subcategories of these categories are introduced consisting of objects $(s u b (A, δ)$ , $σ)$ , where $s u b (A, δ)$ is a subset of all extensional subobjects of an object $(A, δ)$ . It is proved that all these subcategories are quasi-reflective subcategories in the corresponding categories.

Currently displaying 1 – 6 of 6

Page 1

Displaying 1 – 6 of 6

Embeddings of totally ordered MV-algebras of bounded cardinality

Entropy on effect algebras with Riesz decomposition property II: MV-algebras

Entropy on effect algebras with the Riesz decomposition property I: Basic properties

Epimorphisms between finite MV-algebras

Every uniformly Archimedean atomic MV-effect algebra is sharply dominating

Extensional subobjects in categories of Ω -fuzzy sets

Currently displaying 1 – 6 of 6

Extensional subobjects in categories of $Ω$ -fuzzy sets