Editing Analytical hierarchy (section)

{{Short description|Concept in mathematical logic and set theory}}
{{About|the classification of sets|making complex decisions|Analytic hierarchy process}}
In [[mathematical logic]] and [[descriptive set theory]], the '''analytical hierarchy''' is an extension of the [[arithmetical hierarchy]]. The analytical hierarchy of formulas includes formulas in the language of [[second-order arithmetic]], which can have quantifiers over both the set of [[natural numbers]], <math>\mathbb{N}</math>, and over functions from <math>\mathbb{N}</math> to <math>\mathbb{N}</math>. The analytical hierarchy of sets classifies sets by the formulas that can be used to define them; it is the [[lightface]] version of the [[projective hierarchy]].