Strong Medvedev Reducibilities and the KL-Randomness Problem - Kjos-Hanssen, Bjørn; Webb, David J. (Revolutions and Revelations in Computability, 2022)
While it is not known whether each real that is Kolmogorov-Loveland random is Martin-Löf random, i.e., whether KLR⊆MLR $$KLR\subseteq MLR$$ , Kjos-Hanssen and Webb (2021) showed that MLR is truth-table Medvedev reducible (≤s,tt $$\le _{s,tt}$$ ) to KLR. They did this by studying a natural class Either (MLR) and showing that MLR≤s,ttEither(MLR)⊇KLR $$MLR\le _{s,tt}Either\,(MLR)\supseteq KLR$$ . We show that Degtev’s stronger reducibilities (positive and linear) do not suffice for the reduction of MLR to Either (MLR), and some related results.