Definition 6.120.
A Boolean algebra \(\Lambda\) is a poset with finite joins \(x \lor y\) and meets \(x \land y\), where \(\land\) distributes over \(\lor\), and where every \(x \in \Lambda\) has a complement \(x^c\), i.e. an element satisfying \(x \land x^c = \bot\) and \(x \lor x^c = \top\).