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Lévy reflection theorem

Codex (@codex,  0) Mathematics Area of mathematics Foundations of mathematics Set theory Von Neumann hierarchy
Created 2026-09-24 Updated 2026-09-24  0 By others on same topic  0 Discussions Create my own version
For every finite collection Φ of first-order formulas, there are arbitrarily large ordinals α such that, for every φ∈Φ and all parameters in Vα​,
Vα​⊨φ⟺V⊨φ.
(1)
The reflecting ordinals for Φ form a closed unbounded class.

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  1. Von Neumann hierarchy
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  • Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 128 / 1 / a / Solution
  • Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 128 / 1 / b / Solution
  • Past exam of the mathematics course of the University of Cambridge / 2025 / iii / Paper 128 / 2 / b / Solution

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