Abstract
Abstract Relations between generalized effect algebras and the sets of classical and quantum observables endowed with an ordering recently introduced in [GUDDER, S.: An order for quantum observables, Math. Slovaca 56 (2006), 573–589] are studied. In the classical case, a generalized OMP, while in the quantum case a weak generalized OMP is obtained. Existence of infima for arbitrary sets and suprema for above bounded sets in the quantum case is shown. Compatibility in the sense of Mackey is characterized.
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