Definition:Witness Property

Definition
Let $\LL$ be a language of predicate logic.

Let $\MM$ be a formal semantics for $\LL$.

Let $T$ be an $\LL$-theory with respect to $\MM$.

Suppose that, for every WFF of $1$ free variable $\map \phi x$, if:
 * $\FF \models_\MM \exists x : \map \phi x$

then there exists some term $t$ containing no variable such that:
 * $\FF \models_\MM \map \phi {x := t}$

Then, $T$ satisfies the witness property.