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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.

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rdf:type	yago:WikicatMathematicalLogicHierarchies yago:Abstraction100002137 yago:Arrangement107938773 yago:Group100031264 yago:Hierarchy108377806 yago:Ordering108456993 yago:Series108457976
rdfs:label	Analytical hierarchy (en) Jerarquía analítica (es) Hiérarchie analytique (fr) Hierarquia analítica (pt)
rdfs:comment	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. (en) En lógica matemática y teoría descriptiva de conjuntos, la jerarquía analítica es un análogo de alto nivel de la jerarquía aritmética. Por lo tanto constituye la clasificación de los conjuntos mediante las fórmulas que los definen. La jerarquía analítica es importante en teoría de la demostración y aritmética de segundo orden, entre otros campos. (es) En logique mathématique et en théorie de la complexité, la hiérarchie analytique est une extension de la hiérarchie arithmétique définie à partir de formules de la logique du second ordre sur les entiers naturels. * Portail des mathématiques (fr) Na lógica matemática e na Teoria descritiva de conjuntos, a hierarquia analítica é uma extensão da hierarquia aritmética. A hierarquia analítica de fórmulas inclui fórmulas na linguagem da aritmética de segunda ordem, que podem ter quantificadores tanto sobre o conjunto dos números naturais, , quanto sobre as funções de em . A hierarquia analítica de conjuntos classifica-se pelas fórmulas que podem ser utilizadas para defini-las, que é a versão lightface da projeção hierárquica. (pt)
dcterms:subject	Effective descriptive set theory Hierarchy Mathematical logic hierarchies Computability theory
Wikipage page ID	634233 (xsd:integer)
Wikipage revision ID	1105030929 (xsd:integer)
Link from a Wikipage to another Wikipage	Lévy hierarchy Descriptive set theory Analytic set Effective descriptive set theory Hierarchy Mathematical logic hierarchies Mathematical logic Prenex normal form Arithmetical hierarchy Alpha recursion theory Fast-growing hierarchy Logical equivalence Projective hierarchy Baire space (set theory) Hyperarithmetical theory Computability theory Effective Polish space Axiom of constructibility Polish space Natural numbers Cantor space Real number Second-order arithmetic Lightface Boldface (mathematics) Well ordering
Link from a Wikipage to an external page	https://archive.org/details/classicaldescrip0000kech https://archive.org/details/theoryofrecursiv00roge
sameAs	Analytical hierarchy Analytical hierarchy Analytical hierarchy Analytical hierarchy Analytical hierarchy Analytical hierarchy Analytical hierarchy
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has abstract	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. (en) En lógica matemática y teoría descriptiva de conjuntos, la jerarquía analítica es un análogo de alto nivel de la jerarquía aritmética. Por lo tanto constituye la clasificación de los conjuntos mediante las fórmulas que los definen. La jerarquía analítica es importante en teoría de la demostración y aritmética de segundo orden, entre otros campos. (es) En logique mathématique et en théorie de la complexité, la hiérarchie analytique est une extension de la hiérarchie arithmétique définie à partir de formules de la logique du second ordre sur les entiers naturels. * Portail des mathématiques (fr) Na lógica matemática e na Teoria descritiva de conjuntos, a hierarquia analítica é uma extensão da hierarquia aritmética. A hierarquia analítica de fórmulas inclui fórmulas na linguagem da aritmética de segunda ordem, que podem ter quantificadores tanto sobre o conjunto dos números naturais, , quanto sobre as funções de em . A hierarquia analítica de conjuntos classifica-se pelas fórmulas que podem ser utilizadas para defini-las, que é a versão lightface da projeção hierárquica. (pt)
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page length (characters) of wiki page	8771 (xsd:nonNegativeInteger)
foaf:isPrimaryTopicOf	wikipedia-en:Analytical_hierarchy
is Link from a Wikipage to another Wikipage of	List of algorithms Beta-model Reverse mathematics Definable real number Definable set Descriptive set theory Index of philosophy articles (A–C) Kőnig's lemma List of mathematical logic topics List of set theory topics Computability theory Analytic set Prenex normal form George Boolos Glossary of set theory Conservative extension Arithmetical hierarchy Basis theorem (computability) Analytic Wadge hierarchy True arithmetic Fast-growing hierarchy Delta Projective hierarchy Hilary Putnam Hyperarithmetical theory Absoluteness Hierarchy (mathematics) Reduction (computability theory) Axiom of constructibility Borel hierarchy Pi (disambiguation)

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