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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)
##### Keywords:
difference poset; effect algebra; MacNeille completion
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