A first-order formula is syntactically when it is an unbounded existential quantifier block followed by a bounded formula in set theory. Equivalence provable in a specified theory gives the corresponding modulo-theory notion. Existential witnesses show upward absoluteness between transitive models containing the parameters.

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