Modular atomic effect algebras and the existence of subadditive states. (English) Zbl 1249.03120

Riečanová, Zdenka

Kybernetika 40, No. 4, 459-467 (2004).

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)

Keywords:

effect algebra; modular atomic effect algebra; subadditive state; MacNeille completion