Examples
- The set of all prime numbers is arithmetical.
- Every recursively enumerable set is arithmetical.
- Every computable function is arithmetically definable.
- The set encoding the Halting problem is arithmetical.
- Chaitin's constant Ω is an arithmetical real number.
- Tarski's indefinability theorem shows that the set of true formulas of first order arithmetic is not arithmetically definable.
Read more about this topic: Arithmetical Set
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