   Clauses (1) and (2) simply specify what it is for M to be a classical model of the T-free fragment of L. Clauses (3) and (4) ensure that L, when interpreted, can talk about its own sentences.  Given a ground model, we will consider the prospects of providing a satisfying interpretation of T. The most obvious desideratum is that the ground model, expanded to include an interpretation of T, satisfy Tarski's T-biconditionals, i.e., the biconditionals of the form