\begin{definition}[Definition:Cofinal Subset]
Let $\struct {S, \RR}$ be a relational structure, that is, a set $S$ endowed with a binary relation $\RR$.
Let $T \subseteq S$ be a subset of $S$.
Then $T$ is a '''cofinal subset of $S$ with respect to $\RR$''' {{iff}}:
:$\forall x \in S: \exists t \in T: x \mathrel \RR t$
\end{definition}