On the homomorphisms of sum logics
Sylvia Pulmannová, Anatolij Dvurečenskij · French digital mathematics library (Numdam) · 1991
We show that every σ-homomorphism of logics h: L 1 →L 2 , where (L 1 ,S(L 1 )) and (L 2 ,S 2 ) are sum logics [where S(L 1 ) is the set of all σ-additive states on L 1 and S 2 is a quite full set of σ-additive states on L 2 ] is necessarily a lattice σ-homomorphism. Some applications of this statement to Hilbert space logics and projection logics of von Neumann algebras are given