Numberings and Randomness

9 years 3 months ago
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.
Paul Brodhead, Bjørn Kjos-Hanssen
Added 26 May 2010
Updated 26 May 2010
Type Conference
Year 2009
Where CIE
Authors Paul Brodhead, Bjørn Kjos-Hanssen
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