nLab
orthomodular lattice

Contents

Contents

Definition

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

ac a \leq c

implies that

a(a c)=c. 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.