For a set relation in nested transitive models of ZFC, well-foundedness is absolute. An inner-model ordinal rank function witnesses upward absoluteness, and a fixed nonempty subset without a minimal member witnesses failure in both models.

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