Função β de Gödel

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.[1] 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.[2][3][4]

Definição

A função β toma três números naturais como argumentos. É definido como

β(x1, x2, x3) = rem(x1, 1 + (x3 + 1) · x2) = rem(x1, (x3 · x2 + x2 + 1) )

onde rem(x, y) denota o restante após a divisão inteira de x by y (Mendelson 1997:186).

Referências

  1. ↑ O TEOREMA DA INCOMPLETUDE DE GÖDEL EM CURSOS DE LICENCIATURA EM MATEMÁTICA por Batistela, Rosemeire de Fatima (2017)
  2. ↑ Exercicios de Matemtica I por Elan Araújo (2018)
  3. ↑ Elliott Mendelson (1997). Introduction to Mathematical Logic 4th ed. [S.l.]: CRC Press. ISBN 0-412-80830-7 
  4. ↑ Wolfgang Rautenberg (2010). A Concise Introduction to Mathematical Logic 3rd ed. New York: Springer Science+Business Media. p. 244. ISBN 978-1-4419-1220-6. doi:10.1007/978-1-4419-1221-3 
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