The Sixth Lecture on Algorithmic Randomness

This paper follows on from the author’s Five Lectures on Algorithmic Randomness. It is concerned with material not found in that long paper, concentrating on Martin-Lof lowness and triviality. We present a hopefully user-friendly account of the decanter method, and discuss recent results of the author with Peter Cholak and Noam Greenberg concerning the class of strongly jump traceable reals introduced by Figueira, Nies and Stephan.

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