 In 1930 Alfred Tarski formulated the notion of two structures \(A\) and \(B\) being elementarily equivalent, i.e., that exactly the same first-order sentences are true in \(A\) as are true in \(B\). At a conference in Princeton in 1946 he described this notion and expressed the hope that it would be possible to develop a theory of it that would be ‘as deep as the notions of isomorphism, etc. now in use’ (Tarski 1946). 