We prove that superhigh sets can be jump traceable, answering a question of Cole
and Simpson. On the other hand, we show that such sets cannot be weakly
2-random. We also study the class $superhigh^\diamond$ and show that it contains some, but not all, of the noncomputable
K-trivial sets.
Publié le : 2009-10-15
Classification:
Turing degrees,
highness and lowness notions,
algorithmic randomness,
truth-table degrees,
03D28,
03D32,
68Q30
@article{1265899124,
author = {Kjos-Hanssen , Bj\o rn and Nies , Andr\'ee},
title = {Superhighness},
journal = {Notre Dame J. Formal Logic},
volume = {50},
number = {1},
year = {2009},
pages = { 445-452},
language = {en},
url = {http://dml.mathdoc.fr/item/1265899124}
}
Kjos-Hanssen , Bjørn; Nies , Andrée. Superhighness. Notre Dame J. Formal Logic, Tome 50 (2009) no. 1, pp. 445-452. http://gdmltest.u-ga.fr/item/1265899124/