In set theory, a branch of mathematics, the condensation lemma is a result about sets in the constructible 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,
, and the hypothesis of elementarity can be weakened to elementarity only for formulas which are
[1] Also, Devlin showed the assumption that X is transitive automatically holds when
[2] The lemma was formulated and proved by Kurt Gödel in his proof that the axiom of constructibility implies GCH.
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