  Sachs showed that a Boolean algebra is determined by its lattice of
subalgebras. We establish the corresponding result for orthomodular lattices.
We show that an orthomodular lattice L is determined by its lattice of
subalgebras Sub(L), as well as by its poset of Boolean subalgebras BSub(L). The
domain BSub(L) has recently found use in an approach to the foundations of
quantum mechanics initiated by Butterfield and Isham, at least in the case
where L is the orthomodular lattice of projections of a Hilbert space, or von
Neumann algebra. The results here may add some additional perspective to this
line of work.
