On the structure of orthomodular lattices satisfying the chain condition

AbstractBeginning with the external point of view we show how orthomodular lattices may be “pasted” together to yield a new orthomodular lattice. Changing to the internal point of view we show that any two blocks (maximal Boolean suborthomodular lattices) of an orthomodular lattice satisfying the chain condition can be “connected” by blocks which intersect in a specific fashion. Returning to our initial point of view we obtain a method of constructing a given orthomodular lattice from Boolean lattices