 Tarski assumed, in the manner of his time, that the object language \(L\) and the metalanguage \(M\) would be languages of some kind of higher order logic. Today it is more usual to take some kind of informal set theory as one’s metalanguage; this would affect a few details of Tarski’s paper but not its main thrust. Also today it is usual to define syntax in set-theoretic terms, so that for example a string of letters becomes a sequence. In fact one must use a set-theoretic syntax if one wants to work with an object language that has uncountably many symbols, as model theorists have done freely for over half a century now.