\begin{definition}[Definition:Maximal Element/Definition 2]
Let $\struct {S, \RR}$ be a relational structure.
Let $T \subseteq S$ be a subset of $S$.
An element $x \in T$ is a '''maximal element (under $\RR$) of $T$''' {{iff}}:
:$\neg \exists y \in T: x \mathrel {\RR^\ne} y$
where $x \mathrel {\RR^\ne} y$ denotes that $x \mathrel \RR y$ but $x \ne y$.
\end{definition}