Jensen's covering theorem

The first proof appeared in (Devlin & Jensen 1975).

Silver later gave a fine-structure-free proof using his machines[1] and finally Magidor (1990) gave an even simpler proof.

The converse of Jensen's covering theorem is also true: if 0# exists then the countable set of all cardinals less than

cannot be covered by a constructible set of cardinality less than

In his book Proper Forcing, Shelah proved a strong form of Jensen's covering lemma.