ω-change randomness and weak demuth randomness

• Main Authors: Franklin, Johanna N. Y., Ng, Keng Meng
• Other Authors: School of Physical and Mathematical Sciences
• Format: Article
• Language: English
• Published: 2015
• Subjects: DRNTU::Science::Mathematics::Mathematical logic
• Online Access: https://hdl.handle.net/10356/107191; http://hdl.handle.net/10220/25391
• Institution: Nanyang Technological University

We extend our work on difference randomness. Each component of a difference test is a Boolean combination of two r.e. open sets; here we consider tests in which the k th component is a Boolean combination of g(k) r.e. open sets for a given recursive function g. We use this method to produce an alternate characterization of weak Demuth randomness in terms of these tests and further show that a real is weakly Demuth random if and only if it is Martin-Löf random and cannot compute a strongly prompt r.e. set. We conclude with a study of related lowness notions and obtain as a corollary that lowness for balanced randomness is equivalent to being recursive.