Abstract
We prove various results on effective numberings and Friedberg numberings of families related to algorithmic randomness. The family of all Martin-Löf random left-computably enumerable reals has a Friedberg numbering, as does the family of all \(\Pi^0_1\) classes of positive measure. On the other hand, the \(\Pi^0_1\) classes contained in the Martin-Löf random reals do not even have an effective numbering, nor do the left-c.e. reals satisfying a fixed randomness constant. For \(\Pi^0_1\) classes contained in the class of reals satisfying a fixed randomness constant, we prove that at least an effective numbering exists.
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Brodhead, P., Kjos-Hanssen, B. (2009). Numberings and Randomness. In: Ambos-Spies, K., Löwe, B., Merkle, W. (eds) Mathematical Theory and Computational Practice. CiE 2009. Lecture Notes in Computer Science, vol 5635. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03073-4_6
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DOI: https://doi.org/10.1007/978-3-642-03073-4_6
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