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In mathematical logic, Gödel's β function is a function used to permit quantification over finite sequences of natural numbers in formal theories of arithmetic. The β function is used, in particular, in showing that the class of arithmetically definable functions is closed under primitive recursion, and therefore includes all primitive recursive functions.

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  • In mathematical logic, Gödel's β function is a function used to permit quantification over finite sequences of natural numbers in formal theories of arithmetic. The β function is used, in particular, in showing that the class of arithmetically definable functions is closed under primitive recursion, and therefore includes all primitive recursive functions. The β function was introduced without the name in the proof of the first of Gödel's incompleteness theorems (Gödel 1931). The β function lemma given below is an essential step of that proof. Gödel gave the β function its name in (Gödel 1934). (en)
  • En lógica matemática, la función beta de Gödel es una función numérica que permite la definición de funciones recursivas dentro de una teoría formal aritmética. (es)
  • Na lógica matemática, a função β de Gödel é uma função usada para permitir a quantificação sobre seqüências finitas de números naturais em teorias formais da aritmética. A função β é usada, em particular, para mostrar que a classe de funções aritmeticamente definidas é fechada sob recursão primitiva e, portanto, inclui todas as funções recursivas primitivas. (pt)
  • Функция Геделя — функция, применяющаяся в теории алгоритмов для облегчения нумерации множеств натуральных чисел. (ru)
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  • En lógica matemática, la función beta de Gödel es una función numérica que permite la definición de funciones recursivas dentro de una teoría formal aritmética. (es)
  • Na lógica matemática, a função β de Gödel é uma função usada para permitir a quantificação sobre seqüências finitas de números naturais em teorias formais da aritmética. A função β é usada, em particular, para mostrar que a classe de funções aritmeticamente definidas é fechada sob recursão primitiva e, portanto, inclui todas as funções recursivas primitivas. (pt)
  • Функция Геделя — функция, применяющаяся в теории алгоритмов для облегчения нумерации множеств натуральных чисел. (ru)
  • In mathematical logic, Gödel's β function is a function used to permit quantification over finite sequences of natural numbers in formal theories of arithmetic. The β function is used, in particular, in showing that the class of arithmetically definable functions is closed under primitive recursion, and therefore includes all primitive recursive functions. (en)
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  • Función beta de Gödel (es)
  • Gödel's β function (en)
  • Função β de Gödel (pt)
  • Функция Гёделя (ru)
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