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Interpolations in posets and effect algebras. (English) Zbl 1523.06001

Summary: We study various types of the interpolation property in posets and effect algebras. We present connections to other properties of posets and effect algebras (completeness, orthocompleteness, maximality property) and a theorem about preserving compatibility to suprema and infima using an interpolation property.

MSC:

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