Numberings and Randomness

Abstract. We prove various results on effective numberings and Friedberg numberings of families related to algorithmic randomness. The family of all Martin-L¨of random left-computably enumerable reals has a Friedberg numbering, as does the family of all Π0 1 classes of positive measure. On the other hand, the Π0 1 classes contained in the Martin-L¨of random reals do not even have an effective numbering, nor do the left-c.e. reals satisfying a fixed randomness constant. For Π0 1 classes contained in the class of reals satisfying a fixed randomness constant, we prove that at least an effective numbering exists.

• Type: Conference
• Year: 2009
• Where: CIE
• Authors: Paul Brodhead, Bjørn Kjos-Hanssen
• Keywords: Applied Computing, CIE 2009, Effective Numbering, Friedberg Numbering, Reals