Arithmetical hierarchy
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.
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Arithmetical hierarchy
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.
has abstract
Die Arithmetische Hierarchie i ...... metische Hierarchie nach oben.
@de
Em Lógica matemática, a hierar ...... rmulas e conjuntos adicionais.
@pt
En logique mathématique, plus ...... des ensembles récursifs (Δ10).
@fr
In mathematical logic, the ari ...... additional formulas and sets.
@en
La jerarquía aritmética, o jer ...... mulas y conjuntos adicionales.
@es
算术阶层是递归论或可计算性理论中的概念，将自然数的子集按照定义它们的公式的复杂度分类。
@zh
算術的階層（さんじゅつてきかいそう、英: Arithmeti ...... 式や集合の分類の拡張として、超算術的階層や解析的階層がある。
@ja
Wikipage page ID
Wikipage revision ID
737,041,049
subject
type
comment
Die Arithmetische Hierarchie i ...... metische Hierarchie nach oben.
@de
Em Lógica matemática, a hierar ...... a e o conjunto que ela define.
@pt
En logique mathématique, plus ...... nexe qui permet de le définir.
@fr
In mathematical logic, the ari ...... ormula and the set it defines.
@en
La jerarquía aritmética, o jer ...... conjunto que la misma define.
@es
算术阶层是递归论或可计算性理论中的概念，将自然数的子集按照定义它们的公式的复杂度分类。
@zh
算術的階層（さんじゅつてきかいそう、英: Arithmeti ...... 式や集合の分類の拡張として、超算術的階層や解析的階層がある。
@ja
label
Arithmetical hierarchy
@en
Arithmetische Hierarchie
@de
Hierarquia aritmética
@pt
Hiérarchie arithmétique
@fr
Jerarquía aritmética
@es
算数阶层
@zh
算術的階層
@ja