\begin{definition}[Definition:Algebraic Ordered Set]
Let $\left({S, \preceq}\right)$ be an ordered set.
Then $\left({S, \preceq}\right)$ is '''algebraic''' {{iff}}
:(for all elements $x$ of $S$: $x^{\mathrm{compact} }$ is directed) and
:$\left({S, \preceq}\right)$ is up-complete and satisfies axiom of K-approximation
where $x^{\mathrm{compact} }$ denotes the compact closure of $x$.
\end{definition}