Analytical hierarchy
Concept in mathematical logic and set theory / From Wikipedia, the free encyclopedia
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This article is about the classification of sets. For making complex decisions, see 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, , and over functions from
to
. 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.