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, ( X , ∈ ) ≺ ( L α , ∈ ) {\displaystyle (X,\in )\prec (L_{\alpha },\in )} , then in fact there is some ordinal β ≤ α {\displaystyle \beta \leq \alpha } such that X = L β {\displaystyle X=L_{\beta }} .
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, ( X , ∈ ) ≺ ( L α , ∈ ) {\displaystyle (X,\in )\prec (L_{\alpha },\in )} , then in fact there is some ordinal β ≤ α {\displaystyle \beta \leq \alpha } such that X = L β {\displaystyle X=L_{\beta }} .
Source: Wikipedia "Condensation lemma" · CC BY-SA 4.0
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