 The remaining truth definition in Tarski’s 1933 paper – the third as they appear in the paper – is really a bundle of related truth definitions, all for the same object language \(L\) but in different interpretations. The quantifiers of \(L\) are assumed to range over a particular class, call it \(A\); in fact they are second order quantifiers, so that really they range over the collection of subclasses of \(A\). The class \(A\) is not named explicitly in the object language, and thus one can give separate truth definitions for different values of \(A\), as Tarski proceeds to do. So for this section of the paper, Tarski allows one and the same sentence to be given different interpretations; this is the exception to the general claim that his object language sentences are fully interpreted. But Tarski stays on the straight and narrow: he talks about ‘truth’ only in the special case where \(A\) is the class of all individuals. For other values of \(A\), he speaks not of ‘truth’ but of ‘correctness in the domain \(A\)’.