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Modular atomic effect algebras and the existence of subadditive states. (English) Zbl 1249.03120
Summary: Lattice effect algebras generalize orthomodular lattices and MV-algebras. We describe all complete modular atomic effect algebras. This allows us to prove the existence of order-continuous 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 completion is a complete modular effect algebra.

MSC:
03G12 Quantum logic
81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
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