Numberings and Randomness

10 years 14 days 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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