\begin{definition}[Definition:Strictly Maximal Element]
Let $\struct {S, \RR}$ be a relational structure.
Let $T \subseteq S$ be a subset of $S$.
An element $x \in T$ is a '''strictly maximal element under $\RR$ of $T$''' {{iff}}:
:$\forall y \in T: x \not \mathrel \RR y$
\end{definition}