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Uniqueness and order in sequential effect algebras. (English) Zbl 1104.81018

Summary: A sequential effect algebra (SEA) is an effect algebra on which a sequential product is defined. We present examples of effect algebras that admit a unique, many and no sequential product. Some general theorems concerning unique sequential products are proved. We discuss sequentially ordered SEAs in which the order is completely determined by the sequential product. It is demonstrated that intervals in a sequential ordered SEA admit a sequential product.

MSC:

81P10 Logical foundations of quantum mechanics; quantum logic (quantum-theoretic aspects)
03G12 Quantum logic
06C10 Semimodular lattices, geometric lattices
06C15 Complemented lattices, orthocomplemented lattices and posets
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