  Our second theorem comes from the early 20th century. In 1915, Leopold Löwenheim proved that if a first-order sentence has a model, then it has a model whose domain is  countable.[3]  In 1922, Thoralf Skolem generalized this result to whole sets of sentences. He proved that if a countable collection of first-order sentences has an infinite model, then it has a model whose domain is only countable. This is the result which typically goes under the name the Löwenheim-Skolem Theorem. Before moving on, it is useful to mention three, somewhat more refined, versions of this  theorem.[4]