ω-change randomness and weak demuth randomness
Franklin, Johanna N. Y.
Ng, Keng Meng
Date of Issue2014
School of Physical and Mathematical Sciences
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.
The journal of symbolic logic
© 2014 Association for Symbolic Logic. This is the author created version of a work that has been peer reviewed and accepted for publication by The Journal of Symbolic Logic, Association for Symbolic Logic. It incorporates referee’s comments but changes resulting from the publishing process, such as copyediting, structural formatting, may not be reflected in this document. The published version is available at: [http://dx.doi.org/10.1017/jsl.2013.34].