Commutativity in orthomodular posets
Although he finds motivation for his paper in the axiomatic approach to quantum mechanics, of Mackie and Maczynski, the author is here presenting an abstract mathematical discussion of the commutation relation in orthomodular posets. The author gives a very clear and concise summary of previous results, especially as they concern regular, and also Boolean orthomodular posets. He generalises a result due to Guz, showing that if an orthomodular poset P is Boolean, then aCb iff \(a\wedge b\) exists in P. He also presents a method of constructing Boolean orthomodular posets which are not regular - i.e. which have mutually compatible elements which are not contained in a single Boolean subalgebra. Although there is no discussion of physical considerations here, such results are clearly of special interest to those concerned with the axiomatic, or orthomodular, approach to quantum mechanics.
scientific article; zbMATH DE number 3875346