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 .
- Devlin, Keith (1984). Constructibility. Springer. ISBN 3-540-13258-9. (theorem II.5.2 and lemma II.5.10)
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