Analytical hierarchy (original) (raw)
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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| dbo: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) |
| dbo:wikiPageExternalLink | https://archive.org/details/classicaldescrip0000kech https://archive.org/details/theoryofrecursiv00roge |
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| 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) |
| rdfs:label | Analytical hierarchy (en) Jerarquía analítica (es) Hiérarchie analytique (fr) Hierarquia analítica (pt) |
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