Ω-CHANGE RANDOMNESS AND WEAK DEMUTH RANDOMNESS. (18th August 2014)

• Record Type: Journal Article
• Authors: FRANKLIN, JOHANNA N. Y.; NG, KENG MENG
• Is Part Of: Journal of symbolic logic. Volume 79:Number 3(2014)
• Page Start: 776
• Page End: 791
• Publication Date: 2014-08-18
• Subjects: Difference randomness, -- omega-change randomness, -- weak Demuth randomness, -- balanced randomness; Logic, Symbolic and mathematical -- Periodicals; 511.3
• DOI: 10.1017/jsl.2013.34
• Languages: English
• ISSNs: 0022-4812

Abstract

Abstract: 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.