Randomness and immunity.

J. F. Prida

Revista Matemática de la Universidad Complutense de Madrid (1995)

  • Volume: 8, Issue: 2, page 345-351
  • ISSN: 1139-1138

Abstract

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By introducing the concept of randomness through notions of recursion theory, the set of the random numbers is effectively immune. The proof of this well-known result makes an essential use of the recursion theorem. In this paper, randomness is introduced starting from the more common notion of definability in Robinson's arithmetic and the same result is obtained using an extension of the fixed-point theorem, which we prove at the end of the paper. Finally we define a recursive function dominating the set of the random numbers, which consequently is not hyperimmune.

How to cite

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Prida, J. F.. "Aleatoreidad e inmunidad.." Revista Matemática de la Universidad Complutense de Madrid 8.2 (1995): 345-351. <http://eudml.org/doc/44189>.

@article{Prida1995,
author = {Prida, J. F.},
journal = {Revista Matemática de la Universidad Complutense de Madrid},
keywords = {Función recursiva; Lógica matemática; Número aleatorio; Inmunidad; randomness; random numbers; effectively immune; extension of the fixed-point theorem; recursive function},
language = {spa},
number = {2},
pages = {345-351},
title = {Aleatoreidad e inmunidad.},
url = {http://eudml.org/doc/44189},
volume = {8},
year = {1995},
}

TY - JOUR
AU - Prida, J. F.
TI - Aleatoreidad e inmunidad.
JO - Revista Matemática de la Universidad Complutense de Madrid
PY - 1995
VL - 8
IS - 2
SP - 345
EP - 351
LA - spa
KW - Función recursiva; Lógica matemática; Número aleatorio; Inmunidad; randomness; random numbers; effectively immune; extension of the fixed-point theorem; recursive function
UR - http://eudml.org/doc/44189
ER -

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