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MacNeille completions of \(D\)-posets and effect algebras. (English) Zbl 0967.06008
A characterization of difference posets (and hence of effect algebras, too) with MacNeille completion is given by the property of the so-called strong D-continuity. A difference poset \((P,\leq,\ominus,0,1)\) is called strongly D-continuous if for every \(A,B \subseteq P\) such that \(a \leq b\) whenever \(a \in A\) and \(b \in B\) the following condition holds: \(\bigvee \{ b \ominus a \colon\;a \in A,\;b \in B \} = 0\) iff every lower bound of \(B\) is under the upper bound of \(A\).

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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