Extensions of witness mappings (Q1757860)

The paper deals with \textit{interval} effect algebras, i.e., those effect algebras which can be obtained as intervals in partially ordered groups with strong units. A subset of an interval effect algebra \(E\) is said to be coexistent if it is a subset of the range of a homomorphism from a Boolean algebra into~\(E\). As the key result of [the author, Proc. Am. Math. Soc. 139, No. 1, 331--344 (2011; Zbl 1209.03051)], a subset \(S\) of an interval effect algebra~\(E\) is coexistent iff it admits a so-called witness mapping from the collection of finite subsets of~\(S\) into~\(E\). Using this tool, propositions about extensions of coexistent subsets are translated to propositions on extensions of witness mappings.