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Modular atomic effect algebras and the existence of subadditive states

Zdena Riečanová (2004)

Kybernetika

Lattice effect algebras generalize orthomodular lattices and M V -algebras. We describe all complete modular atomic effect algebras. This allows us to prove the existence of ordercontinuous subadditive states (probabilities) on them. For the separable noncomplete ones we show that the existence of a faithful probability is equivalent to the condition that their MacNeille complete modular effect algebra.

Monotone modal operators on bounded integral residuated lattices

Jiří Rachůnek, Zdeněk Svoboda (2012)

Mathematica Bohemica

Bounded integral residuated lattices form a large class of algebras containing some classes of commutative and noncommutative algebras behind many-valued and fuzzy logics. In the paper, monotone modal operators (special cases of closure operators) are introduced and studied.

Monotone σ-complete groups with unbounded refinement

Friedrich Wehrung (1996)

Fundamenta Mathematicae

The real line ℝ may be characterized as the unique non-atomic directed partially ordered abelian group which is monotone σ-complete (countable increasing bounded sequences have suprema), has the countable refinement property (countable sums m a m = n b n of positive (possibly infinite) elements have common refinements) and is linearly ordered. We prove here that the latter condition is not redundant, thus solving an old problem by A. Tarski, by proving that there are many spaces (in particular, of arbitrarily...

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