Extensions of Witness Mappings
Gejza Jen · 2012
We deal with the problem of coexistence in interval effect algebras using the notion of a witness mapping. Suppose that we are given an interval effect algebra E, a coexistent subset S of E, a witness mapping β for S, and an element t ∈ E S. We study the question whether there is a witness mapping βt for S ∪{ t} such that βt is an extension of β. In the main result, we prove that such an extension exists if and only if there is a mapping et from finite subsets of S to E satisfying certain conditions. The main result is then applied several times to prove claims of the type If t has a such-and-such relationship to S and β ,t henβt exists.