An easy priority-free proof of a theorem of Friedberg
Theoretical Computer Science
An introduction to Kolmogorov complexity and its applications (2nd ed.)
An introduction to Kolmogorov complexity and its applications (2nd ed.)
Computability and Randomness
Arithmetic complexity via effective names for random sequences
ACM Transactions on Computational Logic (TOCL)
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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.