If a definable property in a Nonstandard model of Peano arithmetic holds of every standard natural number, then it holds of some nonstandard element. Equivalently, a definable set containing the entire standard cut of a nonstandard model of arithmetic must overspill beyond it.

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  1. Nonstandard model of Peano arithmetic
  2. Peano arithmetic
  3. First-order theory
  4. First-order logic
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