Condensation lemma

In set theory, a branch of mathematics, the condensation lemma is a result about sets in the constructible universe.

It states that if L_α is a level of the constructible hierarchy, X is an elementary submodel of the model $(L_\alpha,\in)$ then $(X,\in)$ is isomorphic to some $(L_\beta,\in)$, $\beta\leq\alpha$.

The lemma was formulated and proved by Kurt Gödel in his proof that the axiom of constructibility implies GCH.

References

• Devlin, Keith (1984). Constructibility. Springer. ISBN 3-540-13258-9. 

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