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We show that an atomic orthomodular lattice L can be reconstructed up toisomorphism from the poset B(L) of Boolean subalgebras of L. A motivation comesfrom quantum theory and the so-called topos approach, where one considers theposet of Boolean sublattices of L=P(H), the projection lattice of the algebraB(H) of bounded operators on Hilbert space.

Reconstructing an atomic orthomodular lattice from the poset of its Boolean sublattices