  Two L-structures that are models of exactly the same sentences of L are said to be elementarily equivalent. Elementary equivalence is an equivalence relation on the class of all L-structures. The set of all the sentences of L that are true in the L-structure A is called the complete theory of A, in symbols Th(A). A theory that is Th(A) for some structure A is said to be complete. (By the completeness theorem for first-order logic, for which see the entry on  classical logic,  a theory is complete if and only if it is maximal syntactically consistent.) The two structures A and B are elementarily equivalent if and only if Th(A) = Th(B).