 Definition 2.5 (Algebraic cpo). A \(D\) is algebraic if, for every \(d \in D\), there is an increasing chain \(x_0 \sqsubseteq x_1 \sqsubseteq \ldots\) of finite approximations of \(d\) such that   \[d = \bigsqcup_n x_n.\]   If \(D\) is algebraic, we say that the finite elements form a basis of \(D\).