If a smaller transitive model has a function witnessing that is a countable set, the same witness exists in every larger transitive model. Downward absoluteness can fail because a larger model may contain a new enumeration of .

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  1. Set-theoretic absoluteness
  2. Formula relativization to a class
  3. Transitive class
  4. Class in set theory
  5. Set theory
  6. Foundations of mathematics
  7. Area of mathematics
  8. Mathematics
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