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.