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.

单词	Covering property
释义	Covering property 英语百科 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.
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Covering property

Jensen's covering theorem