\(\sigma\)-additivity in manuals and orthoalgebras (Q1319086)

The authors define \(\sigma\)-additive orthoalgebras and manuals and characterize \(\sigma\)-additive orthoalgebras as the logic of a \(\sigma\)- additive manual. It can be shown that the orthogonal sum operation of such an orthoalgebra has at most one extension to countable jointly orthogonal sets. Concerning embeddings, it is shown that every orthoalgebra has an embedding in a \(\sigma\)-orthoalgebra and every orthomodular poset can be embedded in a \(\sigma\)-orthomodular poset.