Analytical Hierarchy - The Analytical Hierarchy of Sets of Natural Numbers

The Analytical Hierarchy of Sets of Natural Numbers

A set of natural numbers is assigned the classification if it is definable by a formula. The set is assigned the classification if it is definable by a formula. If the set is both and then it is given the additional classification .

The sets are called hyperarithmetical. An alternate classification of these sets by way of iterated computable functionals is provided by hyperarithmetical theory.

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