Joins and meets in effect algebras

Abstract

It is known that every effect algebra can be represented as the effect algebra of perspectivity classes of some E-test space. We describe when there exists join and meet of two perspectivity classes of events of some algebraic E-test space. Moreover we give the formula for join and meet of perspectivity classes mentioned above, using only tests. We obtain an example of finite, non-homogeneous effect algebra E such that sharp elements of E form a lattice, whereas E is not a lattice.