Definition:Boolean Lattice/Definition 2
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Definition
An ordered structure $\left({S, \vee, \wedge, \preceq}\right)$ is a Boolean lattice if and only if:
$(1): \quad \left({S, \vee, \wedge}\right)$ is a Boolean algebra
$(2): \quad$ For all $a, b \in S$: $a \wedge b \preceq a \vee b$
Also known as
Some sources refer to a Boolean lattice as a Boolean algebra.
However, the latter has a different meaning on $\mathsf{Pr} \infty \mathsf{fWiki}$: see Definition:Boolean Algebra.
Also see
- Results about Boolean lattices can be found here.
Source of Name
This entry was named for George Boole.