 Another result having a somewhat similar force is that of Aerts [1981]. If \(L_1\) and \(L_2\) are two Piron lattices, Aerts constructs in a rather natural way a lattice \(L\) representing two separated systems, each modeled by one of the given lattices. Here “separated” means that each pure state of the larger system \(L\) is entirely determined by the states of the two component systems \(L_1\) and \(L_2\). Aerts then shows that \(L\) is again a Piron lattice iff at least one of the two factors \(L_1\) and \(L_2\) is classical. (This result has recently been strengthened by Ischi [2000] in several ways.)