For finite, these sets are closely related to the arithmetic hierarchy.
2.
So far down in the arithmetic hierarchy, and that goes for any recursively axiomatized ( countable, consistent ) theories.
3.
This classic proof is a very early, original application of the arithmetic hierarchy theory to a general-logical problem.
4.
Note that we can also define the arithmetic hierarchy of subsets of the Cantor and Baire spaces relative to some set of integers.
5.
Note that while both the elements of the Cantor space ( regarded as sets of integers ) and subsets of the Cantor space are classified in arithmetic hierarchies, these are not the same hierarchy.
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