In set theory, Jensen's covering theorem states that if 0# does not exist then every uncountable set of ordinals is contained in a constructible set of the same cardinality. Informally this conclusion says that the constructible universe is close to the universe of all sets. The first proof appeared in . Silver later gave a fine structure free proof using his machines and finally Magidor gave an even simpler proof. In his book Proper Forcing, Shelah proved a strong form of Jensen's covering lemma.