Definition:Boolean Lattice

Definition 1
A Boolean lattice is a complemented distributive lattice.

Definition 2
An ordered structure $\left({S, \vee, \wedge, \preceq}\right)$ is a Boolean lattice iff:

$(1): \quad \left({S, \vee, \wedge}\right)$ is a Boolean algebra

$(2): \quad$ For all $a, b \in S$: $a \wedge b \preceq a \vee b$

Equivalence of Definitions
That the definitions given above are equivalent is shown on Equivalence of Boolean Lattice Definitions.

Also see

 * Boolean Algebra