\begin{definition}[Definition:Indiscernible]
Let $\MM$ be an $\LL$-structure.
Let $I$ be an infinite set.
Let $X = \set {x_i \in \MM: i \in I}$ be an infinite subset of the universe of $\MM$ indexed by $I$.
For:
:every $n \in \N$
and:
:every pair of subsets $\set {i_1, \ldots, i_n}$ and $\set {j_1, \ldots, j_n}$ of $I$ each with $n$ distinct elements,
Let:
:$\MM \models \map \phi {x_{i_1}, \ldots, x_{i_n} } \leftrightarrow \map \phi {x_{j_1}, \ldots, x_{j_n} }$ for all $\LL$-formulas $\phi$ with $n$ free variables.
Then $X$ is '''(an) indiscernible (set) in $\MM$'''.
Informally, $X$ is '''indiscernible (set)''' {{iff}} $\MM$ cannot distinguish between same-sized ordered tuples over $X$ using $\LL$-formulas.
\end{definition}