About: Jensen's covering theorem

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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.

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  • 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. The converse of Jensen's covering theorem is also true: if 0# exists then the countable set of all cardinals less than ℵω cannot be covered by a constructible set of cardinality less than ℵω. In his book Proper Forcing, Shelah proved a strong form of Jensen's covering lemma. (en)
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  • 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. (en)
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  • Jensen's covering theorem (en)
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