论文标题
强大的梅德韦杰夫还原性和KL随机问题
Strong Medvedev reducibilities and the KL-randomness problem
论文作者
论文摘要
虽然尚不清楚每个真实的都是kolmogorov-loveland随机是随机的，即$ \ mathrm {klr} \ subseteq \ subseteq \ mathrm {mlr} $，kjos-hanssen and kjos-hanssen and webb（2021）都表明了$ \ m m i \ mathrm {mlr} $ {mlr} （$ \ le_ {s，tt} $）to $ \ mathrm {klr} $。他们通过研究自然班（MLR）来做到这一点，并表明$ \ mathrm {mlr} \ le_ {s，tt} \ mathrm {tocte \ supseteq \ supseteq \ mathrm {klr} $。我们表明，DEGTEV的更强的还原性（正线性和线性）不足以将MLR降低到（MLR）和一些相关的结果。
While it is not known whether each real that is Kolmogorov-Loveland random is Martin-Löf random, i.e., whether $\mathrm{KLR}\subseteq\mathrm{MLR}$, Kjos-Hanssen and Webb (2021) showed that $\mathrm{MLR}$ is truth-table Medvedev reducible ($\le_{s,tt}$) to $\mathrm{KLR}$. They did this by studying a natural class Either(MLR) and showing that $\mathrm{MLR}\le_{s,tt}\mathrm{Either(MLR)}\supseteq\mathrm{KLR}$. 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.
