  If L is the first-order language of signature K, then  Tarski’s model-theoretic truth definition tells us when a sentence of L is true in A, and when an assignment of elements of A to variables satisfies a formula of L in A. Instead of talking of assignments satisfying a formula, model theorists often speak of the set of n-tuples of elements of A that is defined by a formula φ(v1,…,vn); the connection is that an n-tuple (a1,…,an) is in the defined set if and only if the assignment taking each vi to ai satisfies the formula.