Displaying similar documents to “Entropy on effect algebras with the Riesz decomposition property I: Basic properties”

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

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

Kybernetika

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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.

A spectral theorem for σ MV-algebras

Sylvia Pulmannová (2005)

Kybernetika

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MV-algebras were introduced by Chang, 1958 as algebraic bases for multi-valued logic. MV stands for “multi-valued" and MV algebras have already occupied an important place in the realm of nonstandard (mathematical) logic applied in several fields including cybernetics. In the present paper, using the Loomis–Sikorski theorem for σ -MV-algebras, we prove that, with every element a in a σ -MV algebra M , a spectral measure (i. e. an observable) Λ a : ℬ ( [ 0 , 1 ] ) → ℬ ( M ) can be associated, where ℬ ( M ) denotes the Boolean...

A Cantor-Bernstein theorem for σ -complete MV-algebras

Anna de Simone, Daniele Mundici, Mirko Navara (2003)

Czechoslovak Mathematical Journal

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The Cantor-Bernstein theorem was extended to σ -complete boolean algebras by Sikorski and Tarski. Chang’s MV-algebras are a nontrivial generalization of boolean algebras: they stand to the infinite-valued calculus of Łukasiewicz as boolean algebras stand to the classical two-valued calculus. In this paper we further generalize the Cantor-Bernstein theorem to σ -complete MV-algebras, and compare it to a related result proved by Jakubík for certain complete MV-algebras.