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In set theory, a branch of mathematics, th … 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. Also, the assumption that X be transitive automatically holds when . The lemma was formulated and proved by Kurt Gödel in his proof that the axiom of constructibility implies GCH.the axiom of constructibility implies GCH.
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In set theory, a branch of mathematics, th … 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. Also, the assumption that X be transitive automatically holds when .X be transitive automatically holds when .
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Condensation lemma
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