Representable Effect Algebras and Observables

We introduce a class of monotone sigma-complete effect algebras, called representable, which are sigma-homomorphic images of a class of monotone sigma-complete effect algebras of functions taking values in the interval [0, 1] and with effect algebra operations defined by points. We exhibit different types of compatibilities and show their connection to representability. Finally, we study observables and show situations when information of an observable on all intervals of the form (-a, t) gives full information about the observable.