Arithmetical hierarchy (nonfiction): Difference between revisions
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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:
- Arithmetical hierarchy @ Wikipedia