#
nLab

orthomodular lattice

### Context

#### $(0,1)$-Category theory

# Contents

## 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 14:14:27.
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