  The first work containing a mathematical definition of one of the semantical notions is Tarski (1931) (English version, Tarski 1983d), where Tarski examines a language L in which it is possible to formalize the arithmetic of the real numbers, and gives a recursive definition of the notion “set of real numbers definable in L” (cf. Def. 9 in Tarski 1983d, p. 128). The definition depends on others that are a bit cumbersome; today we would define a similar notion in a simpler way with the help of the definition of truth that Tarski himself would publish two years later. But the essence of the Tarskian definition of truth is already here. In the 1931 paper we find also, as was to be expected, the Tarskian concern with matters of precision and foundational rigor, and a revealing statement about the attitude of mathematicians toward the notion of definability, that could be extended to other semantical notions: