 The reservation is that Tarski’s definition of satisfaction in the 1933 paper doesn’t in fact mention the class of assignments that satisfy a formula \(F\). Instead, as we saw, he defines the relation ‘\(a\) satisfies \(F\)’, which determines what that class is. This is probably the main reason why some people (including Tarski himself in conversation, as reported by Barbara Partee) have preferred not to describe the 1933 definition as compositional. But the class format, which is compositional on any reckoning, does appear in an early variant of the truth definition in Tarski’s paper of 1931 on definable sets of real numbers. Tarski had a good reason for preferring the format ‘\(a\) satisfies \(F\)’ in his 1933 paper, namely that it allowed him to reduce the set-theoretic requirements of the truth definition. In sections 4 and 5 of the 1933 paper he spelled out these requirements carefully.