User:Jshflynn/Definition:Formal language

Definition
Let $\Sigma$ be an alphabet.

Let $\mathcal{P}(\Sigma^{*})$ denote the $P$-star of $\Sigma$.

Let $V \subseteq \mathcal{P}(\Sigma^{*})$.

Then $V$ is a formal language (or just language) over $\Sigma$.