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Definition

An orthomodular lattice is an orthocomplemented lattice in which in addition a weak form of modularity holds in that

$a \leq c$

implies that

$a \vee (a^\perp \wedge c) = c \,.$

Examples

The canonical example are the Hilbert lattices that interpret Birkhoff-vonNeumann quantum logic.

References

• P. Pták and S. Pulmannová, Orthomodular structures as quantum logics, ser. Fundamental theories of physics. Kluwer Academic Publishers, 1991.

Created on February 28, 2014 at 14:14:29. See the history of this page for a list of all contributions to it.