Definable Set

A definable set of an $\mathcal{L}$ theory $T$ in a First-Order Language is an equivalence class of formulas that evaluate to the same truth value in every model of $T$.

Note that Schemes do not play as much of a role here, as model theory is fundamentally Proof-Irrelevant; see https://math.stackexchange.com/questions/2869455/applications-of-model-theory-where-are-the-sheaves for information on the topological view on this.