Model
# Definition
Let $\mathcal{L}$ be a Language, let $\mathcal{M}$ be an $\mathcal{L}$-Language Structure, and let $T$ be an $\mathcal{L}$-Theory. We say $\mathcal{M}$ is a Model of $T$ and write $\mathcal{M} \models T$ if $\mathcal{M} \models \phi$ for all $\phi \in T$.