1306.1950 (Carmen Constantin et al.)

Reconstructing an atomistic ortholattice from the poset of its Boolean
sublattices    [PDF]

Carmen Constantin, Andreas Doering

We show that an atomistic ortholattice L can be reconstructed up to isomorphism from the poset B(L) of Boolean subalgebras of L. A motivation comes from quantum theory and the so-called topos approach, where one considers the poset of Boolean sublattices of L=P(H), the projection lattice of the algebra L(H) of bounded operators on Hilbert space.

View original: http://arxiv.org/abs/1306.1950