Definition:Minimal Element/Definition 2

Definition
Let $\struct {S, \RR}$ be a relational structure.

Let $T \subseteq S$ be a subset of $S$.

An element $x \in T$ is a minimal element (under $\RR$) of $T$ :
 * $\neg \exists y \in T: y \mathrel {\RR^\ne} x$

where $y \mathrel {\RR^\ne} x$ denotes that $y \mathrel \RR x$ but $y \ne x$.

Also see

 * Equivalence of Definitions of Minimal Element