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

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

Czechoslovak Mathematical Journal

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.

A groupoid characterization of orthomodular lattices

Ivan Chajda (2005)

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

We prove that an orthomodular lattice can be considered as a groupoid with a distinguished element satisfying simple identities.

A measure-theoretic characterization of Boolean algebras among orthomodular lattices

Pavel Pták, Sylvia Pulmannová (1994)

Commentationes Mathematicae Universitatis Carolinae

We investigate subadditive measures on orthomodular lattices. We show as the main result that an orthomodular lattice has to be distributive (=Boolean) if it possesses a unital set of subadditive probability measures. This result may find an application in the foundation of quantum theories, mathematical logic, or elsewhere.

A new approach to representation of observables on fuzzy quantum posets

Le Ba Long (1992)

Applications of Mathematics

We give a representation of an observable on a fuzzy quantum poset of type II by a pointwise defined real-valued function. This method is inspired by that of Kolesárová [6] and Mesiar [7], and our results extend representations given by the author and Dvurečenskij [4]. Moreover, we show that in this model, the converse representation fails, in general.

A note on the symmetric difference in lattices.

Eloy Renedo, Enric Trillas, Claudio Alsina (2005)

Mathware and Soft Computing

The paper introduces a definition of symmetric difference in lattices with negation, presents its general properties and studies those that are typical of ortholattices, orthomodular lattices, De Morgan and Boolean algebras.

A remark on λ -regular orthomodular lattices

Vladimír Rogalewicz (1989)

Aplikace matematiky

A finite orthomodular lattice in which every maximal Boolean subalgebra (block) has the same cardinality k is called λ -regular, if each atom is a member of just λ blocks. We estimate the minimal number of blocks of λ -regular orthomodular lattices to be lower than of equal to λ 2 regardless of k .

A short note on lattices allowing disjunctive reasoning.

Enric Trillas, Eloy Renedo, Claudi Alsina (2006)

Mathware and Soft Computing

This short note shows that the scheme of disjunctive reasoning, a or b, not b : a, does not hold neither in proper ortholattices nor in proper de Morgan algebras. In both cases the scheme, once translated into the inequality b' · (a+b) ≤ a, forces the structure to be a boolean algebra.

An atomic MV-effect algebra with non-atomic center

Vladimír Olejček (2007)


Does there exist an atomic lattice effect algebra with non-atomic subalgebra of sharp elements? An affirmative answer to this question (and slightly more) is given: An example of an atomic MV-effect algebra with a non-atomic Boolean subalgebra of sharp or central elements is presented.

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