  Tarski uses a certain precise notion of interpretation for a formal language. In our example, an interpretation of LAr is a sequence &lt;A, a, R&gt; that assigns appropriate objects to the non-logical constants of LAr: a set of individuals A to “N”, an individual a to “0” and a binary relation among individuals R to “M”. Besides, he always requires that the objects assigned by an interpretation to the other non-logical constants of a language be drawn from the set assigned to the non-logical predicate that restricts the range of quantification to a specific set of individuals (“N” in the case of LAr) (cf.  Tarski 1937, §34); so in the case of LAr the individual assigned to “0” must belong to the set assigned to “N” and the relation assigned to “M” must be a relation among objects in the set assigned to “N”.