Jensen's covering theorem

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 (Devlin & Jensen 1975). Silver later gave a fine structure free proof using his machines and finally Magidor (1990) gave an even simpler proof.