Sequential products on effect algebras

A sequential effect algebra (SEA) is an effect algebra on which a sequential product with natural properties is defined. The properties of sequential products on Hilbert space effect algebras are discussed. For a general SEA, relationships between sequential independence, coexistence and compatibility are given. It is shown that the sharp elements of a SEA form an orthomodular poset. The sequential center of a SEA is discussed and a characterization of when the sequential center is isomorphic to a fuzzy set system is presented. It is shown that the existence, of a sequential product is a strong restriction that eliminates many effect algebras from being SEAʹs. For example, there are no finite nonboolean SEAʹs, A measure of sharpness called the sharpness index is studied. The existence of horizontal sums of SEAʹs is characterized and examples of horizontal sums and tensor products are presented.