Compatibility support mappings in effect algebras (Q2883984)

Effect algebras [\textit{D. J. Foulis} and \textit{M. K. Bennett}, Found. Phys. 24, 1331--1352 (1994; Zbl 1213.06004)] were introduced as an abstraction of the set of Hilbert space effects, i.e., operators between \(0\) and \(I\) on a Hilbert space, which play an important role in the description of quantum measurements. A very important question is: what sets of effects can be measured simultaneously? On an abstract algebraic level this question can be reformulated as follows: If \(S\) is a subset of an effect algebra \(E\), is there a Boolean algebra \(B\) and an effect-algebra morphism from \(B\) to \(E\) such that \(S\) is a subset of the image of \(B\)? In the paper, the question is answered by means of so-called compatibility support mappings, which are mappings from the product of \({\operatorname {Fin}(S)}\) with itself to \(E\) with certain properties. Compatibility support mappings are compared with witness mappings introduced previously by the author [Proc. Am. Math. Soc. 139, 331--344 (2011; Zbl 1209.03051)].