Lattices with Unique Complements

For several years one of the outstanding problems of lattice theory has been the following: Is every lattice with unique complements a Boolean algebra? Any number of weak additional restrictions are sufficient for an affirmative answer. For example, if a lattice is modular (G. Bergman [1](1)) or ortho-complemented (G. Birkhoff [1]) or atomic (G. Birkhoff and M. Ward [1]), then unique complementation implies distributivity and the lattice is a Boolean algebra.