Displaying similar documents to “On the permanence properties of interval homogeneous orthomodular lattices”

Orthocomplemented difference lattices with few generators

Milan Matoušek, Pavel Pták (2011)

Kybernetika

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The algebraic theory of quantum logics overlaps in places with certain areas of cybernetics, notably with the field of artificial intelligence (see, e. g., [19, 20]). Recently an effort has been exercised to advance with logics that possess a symmetric difference ([13, 14]) - with so called orthocomplemented difference lattices (ODLs). This paper further contributes to this effort. In [13] the author constructs an ODL that is not set-representable. This example is quite elaborate. A...

A measure-theoretic characterization of Boolean algebras among orthomodular lattices

Pavel Pták, Sylvia Pulmannová (1994)

Commentationes Mathematicae Universitatis Carolinae

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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.

Cantor-Bernstein theorem for lattices

Ján Jakubík (2002)

Mathematica Bohemica

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This paper is a continuation of a previous author’s article; the result is now extended to the case when the lattice under consideration need not have the least element.