  In spite of this, the results about semantical notions were important and even moderately abundant by 1930. Among these Tarski himself would mention Gödel’s completeness theorem and several versions of the Löwenheim-Skolem theorem (cf. Tarski 1983b, pp. 240–1, sp. p. 240 n.1, and p. 241 n. 2). All these results use the notion of truth in a structure, or functionally equivalent notions. And Tarski says that