 Inspired by the rather brief treatment of first-order statements about relations in Vol. III of the Algebra der Logik, Löwenheim (1915) showed that if such a statement could be satisfied in an infinite domain then it could be satisfied in a denumerable domain. In 1920 Thoralf Skolem (1887–1963) simplified Löwenheim’s proof by introducing Skolem normal forms, and in 1928 Skolem replaced his use of normal forms with a simpler idea, namely to use what are now called Skolem functions. He used these functions to convert first-order sentences into universal sentences, that is to say, into sentences in prenex form with all quantifiers being universal (\(\forall\)).