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.
@article{urn:eudml:doc:44189,
title = {Aleatoreidad e inmunidad.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {8},
year = {1995},
pages = {345-351},
zbl = {0857.03024},
mrnumber = {MR1367935},
language = {es},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44189}
}
Prida, J. F. Aleatoreidad e inmunidad.. Revista Matemática de la Universidad Complutense de Madrid, Tome 8 (1995) pp. 345-351. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44189/