The representation of Takeuti's \(\coprod\)-operator (Q798319)

\textit{G. Takeuti} has recently proposed [Current issues in quantum logic, 303-322 (1981; Zbl 0537.03044)] a new operation on orthomodular lattices L, \(\coprod: {\mathcal P}(L)\to L.\) The properties of \(\coprod\) suggest that the value of \(\coprod (A) (A\subseteq L)\) corresponds to the degree in which the elements of A behave classically. To make this idea precise, we investigate the connection between structural properties of orthomodular lattices L and the existence of two-valued homomorphisms on L. \(\{\) Cor. 4.3(c) is wrong and will be corrected in the next issue of Stud. Logic\(a\}\).