Arithmetical hierarchy (nonfiction): Difference between revisions

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== Nonfiction cross-reference ==
== Nonfiction cross-reference ==


* [[Mathematics (fiction)]]
* [[Mathematics (nonfiction)]]
* [[Set theory (nonfiction)]]


External links:
External links:
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[[Category:Nonfiction (nonfiction)]]
[[Category:Nonfiction (nonfiction)]]
[[Category:Complexity (nonfiction)]]
[[Category:Mathematics (nonfiction)]]
[[Category:Mathematics (nonfiction)]]
[[Category:Set theory (nonfiction)]]

Latest revision as of 21:20, 17 April 2017

In mathematical logic, the arithmetical hierarchy, arithmetic hierarchy, or Kleene–Mostowski hierarchy classifies certain sets based on the complexity of formulas that define them. Any set that receives a classification is called arithmetical.

The arithmetical hierarchy is important in recursion theory, effective descriptive set theory, and the study of formal theories such as Peano arithmetic.

The Tarski-Kuratowski algorithm provides an easy way to get an upper bound on the classifications assigned to a formula and the set it defines.

The hyperarithmetical hierarchy and the analytical hierarchy extend the arithmetical hierarchy to classify additional formulas and sets.

Fiction cross-reference

Nonfiction cross-reference

External links: