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- Condensation_lemma abstract "In set theory, a branch of mathematics, the condensation lemma is a result about sets in theconstructible universe.It states that if X is a transitive set and is an elementary submodel of some level of the constructible hierarchy Lα, that is, , then in fact there is some ordinal such that .More can be said: If X is not transitive, then its transitive collapse is equal to some , and the hypothesis of elementarity can be weakened to elementarity only for formulas which are in the Lévy hierarchy.The lemma was formulated and proved by Kurt Gödel in his proof that the axiom of constructibility implies GCH.".
- Condensation_lemma wikiPageID "20506691".
- Condensation_lemma wikiPageRevisionID "565759911".
- Condensation_lemma hasPhotoCollection Condensation_lemma.
- Condensation_lemma subject Category:Lemmas.
- Condensation_lemma subject Category:Set_theory.
- Condensation_lemma type Abstraction100002137.
- Condensation_lemma type Communication100033020.
- Condensation_lemma type Lemma106751833.
- Condensation_lemma type Lemmas.
- Condensation_lemma type Message106598915.
- Condensation_lemma type Proposition106750804.
- Condensation_lemma type Statement106722453.
- Condensation_lemma comment "In set theory, a branch of mathematics, the condensation lemma is a result about sets in theconstructible universe.It states that if X is a transitive set and is an elementary submodel of some level of the constructible hierarchy Lα, that is, , then in fact there is some ordinal such that .More can be said: If X is not transitive, then its transitive collapse is equal to some , and the hypothesis of elementarity can be weakened to elementarity only for formulas which are in the Lévy hierarchy.The lemma was formulated and proved by Kurt Gödel in his proof that the axiom of constructibility implies GCH.".
- Condensation_lemma label "Condensation lemma".
- Condensation_lemma sameAs m.04zx6yj.
- Condensation_lemma sameAs Q5159176.
- Condensation_lemma sameAs Q5159176.
- Condensation_lemma sameAs Condensation_lemma.
- Condensation_lemma wasDerivedFrom Condensation_lemma?oldid=565759911.
- Condensation_lemma isPrimaryTopicOf Condensation_lemma.